Method for dual harmonization of a ddp posture-detecting subsystem integrated into a worn/borne head-up viewing system

ABSTRACT

A method for dual harmonization of a DDP posture-detecting subsystem integrated into a worn/borne head-up viewing system includes a first step of measurements of N rotation matrices {circumflex over (K)}i for detecting the posture of a head corresponding to a set of different targeting actions Vi, in which measurements one or more different preset elements of pilot/driver information displayed in the viewing device Dv are superposed or aligned with one or more corresponding landmarks of the real outside world; then a second step of conjointly calculating the relative orientation matrix {circumflex over (R)}(S1/v) of the DDP tracking first element S1 with respect to the viewing device Dv and/or the relative orientation matrix {circumflex over (R)}(ref/S2) of the external reference device DRef with respect to the DDP fixed solid second element S2 to respectively be the right-side bias rotation matrix {circumflex over (D)} and the left-side bias rotation matrix Ĝ, which are solutions of the system of dual harmonization equations: Ûi=Ĝ·{circumflex over (K)}i·{circumflex over (D)}, i varying from 1 to N.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority to foreign French patent application No. FR 1701343, filed on Dec. 21, 2017, the disclosure of which is incorporated by reference in its entirety.

FIELD OF THE INVENTION

The present invention relates to a method and subsystem for dual harmonization of a DDP (acronym of the French expression detection de posture) posture-detecting subsystem integrated into a worn/borne head-up viewing system.

BACKGROUND

The worn/borne head-up viewing system and posture-detecting subsystem are intended to be located on-board carrier vehicles that are able to move with respect to a reference coordinate system of a real outside world. These vehicles are in particular aircraft, military or civilian aeroplanes or military or civilian helicopters.

In any case, the purpose of the posture-detecting subsystem is to make available, to the pilot/driver or to the worn/borne head-up viewing system, the angular orientation or the relative rotation between a tracking mobile solid first element S1 that is associated with the head of the pilot, and a fixed solid second element S2 that is associated either with the coordinate system of the platform of the aircraft, or with the local geographic coordinate system, or with a terrestrial coordinate system.

Generally, a posture-detecting subsystem is configured to make available to the pilot/driver or to the piloting/driving system information on the relative three-dimensional 3D rotation between:

-   on the one hand a tracking mobile first element S1 of said DDP     posture-detecting system, which element is solid and orientable with     three angles of rotation, and has a first orthonormal coordinate     system R_(S1) that is tightly linked to a transparent viewing device     D_(v) allowing, simultaneously, pilot/driver information (images,     symbols, instructions, reticles) to be displayed in a coordinate     system R_(v) called the viewing or targeting coordinate system, and     observation of objects of a real outside world; and -   on the other hand a fixed second element S2 of said DDP     posture-detecting subsystem, which element is solid, has a second     orthonormal coordinate system R_(S2) and is tightly linked to a     reference device D_(ref) having what is called a reference     coordinate system, designated by R_(ref), and able to be either a     coordinate system of the carrier vehicle, or a local geographic     coordinate system, or a terrestrial coordinate system.

By definition, a “tight” link between the orientable solid first element S1 of the DDP posture-detecting subsystem and the viewing and targeting device D_(v) is a rigid link that ensures that the rotation matrix {circumflex over (R)}(R_(S1)/R_(v)) allowing passage from the first orthonormal coordinate system R_(S1), which is attached to the orientable tracking solid first element S1 of the posture-detecting subsystem, to the viewing and targeting coordinate system R_(v) is a rotation matrix that is invariant in time.

By definition, a “tight” link between the solid second element S2 of the DDP posture-detecting subsystem and the fixed reference device D_(ref) is a rigid link that ensures that the rotation matrix {circumflex over (R)}(R_(S1)/R_(v)) allowing passage from the second orthonormal coordinate system R_(S2), which is attached to the fixed solid second element S2 of the posture-detecting subsystem, to the fixed coordinate system R_(ref) is a rotation matrix that is invariant in time.

Often, the fixed reference coordinate system R_(ref) is the coordinate system in which the coordinates of objects that it is desired to observe in the viewing and aligning coordinate system R_(v) associated with the viewing and targeting system are known. The DDP posture-detecting subsystem then allows real or virtual objects to be “projected” from the reference coordinate system into the viewing coordinate system. In particular, if this system is transparent, it is possible to superpose the projected objects on their real image, conformal projection then being spoken of.

In any case, the useful output information DDP_(useful) that it is sought to deliver to the pilot/driver or to the piloting/driving device, i.e. the rotation between the coordinate system R_(v) of the sight of the helmet/headset of the pilot/driver and the reference coordinate system R_(ref) is different from the raw output DDP_(raw) calculated by the DDP posture-detecting system, i.e. the measured and calculated rotation matrix between a first orthonormal coordinate system R_(S1), which is tightly linked to the pointing and viewing coordinate system R_(v), and a second orthonormal coordinate system R_(S2), which is tightly linked to the reference coordinate system R_(ref).

Generally, the rotation DDP_(raw) calculated by way of its matrix by the posture-detecting system is inexact, i.e. different from the actual rotation between the coordinate system R_(v) of the sight of the helmet/headset of the pilot/driver and the reference coordinate system R_(ref), this rotation also being called the useful output rotation DDP_(useful).

The calculated raw output rotation DDP_(raw) calculated by the DDP posture-detecting system is inexact in particular for the following reasons, which are not exclusive from one another, more than one possibly being applicable:

-   the raw output DDP_(raw) calculated by the DDP posture-detecting     system, which expresses the rotation between a first coordinate     system R_(S1) of the orientable first element S1 of the DDP and a     second coordinate system R_(S2) of the solid second element S2 of     the DDP is different from the useful output rotation DDP_(useful)     between the desired coordinate system R_(v) of the sight of the     helmet/headset of the pilot/driver or of the pointing device; -   the calculated raw output DDP_(raw) is only partially defined, one     or more of its matrix components being missing; -   the calculated raw output DDP_(raw) has been altered by the     appearance of a bias or offset, for example following a shock or     ageing or a poorly aligned installation.

At the present time, to make the calculated raw output DDP_(raw) more exact, it is known to carry out correctional alignments, but these correctional alignments are partial and work only for a single bias, or a single identified unknown, and provided that only this one bias defect exists.

In addition, when a posture detection error is observed, for example by observing a nonconformity, it is difficult, or even impossible, depending on the circumstances, to identify the error and to correct the calculated raw output DDP_(raw), because of the fact that the posture detection defect expresses itself locally by a double possible alteration of the calculated raw output matrix DDP_(raw), i.e. one to the left by a left rotation matrix denoted Ĝ, and one to the right by a right rotation matrix denoted {circumflex over (D)}, the rotation matrices DDP_(useful), DDP_(raw), Ĝ and {circumflex over (D)} being related by the following relationship:

DDP _(useful) =Ĝ·DDP _(raw) ·{circumflex over (D)}

-   in which the useful output matrix DDP_(useful), the raw output     matrix DDP_(raw), the left rotation matrix Ĝ, and the right rotation     matrix {circumflex over (D)} respectively satisfy the following     relationships:

DDP _(useful) ={circumflex over (R)}(R _(ref) /R _(v))

DDP _(raw) ={circumflex over (R)}(R _(S2) /R _(S1))

Ĝ={circumflex over (R)}(R _(ref))/R _(S2))

{circumflex over (D)}={circumflex over (R)}(R _(S1)/R _(v)).

At the present time, proposed solutions for harmonizing the raw output matrix DDP_(raw) consist of complex algorithms that include at least two steps, each step corresponding to a partial harmonization of a limited number of components of the raw output matrix, the remaining components, which are not harmonized, needing to be perfectly known as otherwise residual defects alter the result of the harmonization in progress. Thus, it is not possible to achieve a dual optimization of defects. In other words, the harmonization methods proposed and carried out at present are complex methods that separately determine the two, left and right, rotation matrices Ĝ and {circumflex over (D)}, and therefore that do not allow a dual optimization of defects.

Moreover, current-day harmonization methods make excessive use of trigonometry functions, which are sources of imprecision and multiple errors, and which are not needed to harmonize a raw output of a posture-detecting system.

SUMMARY OF THE INVENTION

The technical problem that the invention solves is that of remedying the aforementioned drawbacks and of providing a method for dual harmonization of the raw output rotation measured and calculated by a posture-detecting system that determines, in a global way, i.e., at the same time, the left and right rotation matrices Ĝ and {circumflex over (D)}.

Particularly, the technical problem is to provide a method for global harmonization of the raw output rotation matrix measured and calculated by a posture-detecting system, which implements a single set of measurement stations without knowledge of sources of alteration.

The provided solution allows, with a single set of measurements, the useful DDP output to be calculated whether the origin of the alterations is known in advance or not.

To this end, one subject of the invention is a method for dual harmonization of a DDP posture-detecting subsystem integrated into a worn/borne head-up viewing system, the worn/borne head-up viewing system being located on-board a carrier vehicle and comprising: a transparent worn/borne head-up viewing device D_(v), an exterior reference device D_(ref) having an exterior reference coordinate system R_(ref), possibly either a coordinate system of the carrier vehicle or a local geographic coordinate system or a terrestrial coordinate system; a DDP posture-detecting subsystem comprising a tracking solid first element S1 rigidly and tightly attached to the viewing device D_(v), a fixed solid second element S2 tightly joined to the reference device D_(ref), and a means for measuring and determining the relative orientation {circumflex over (K)} of the tracking mobile first element S1 with respect to the fixed second element S2; a dual harmonization subsystem for harmonizing the worn/borne head-up viewing system and the DDP posture-detecting subsystem.

The dual harmonization method is characterized in that it comprises steps consisting in:

-   in a first step, a series of a preset number N of measurements of     relative orientations {circumflex over (K)}_(i), i varying from 1 to     N, of the tracking mobile first element S1 with respect to the fixed     second element S2 of the DDP posture-detecting subsystem,     corresponding to different targeting actions Vi, i varying from 1 to     N, are carried out, in which measurements one or more different     preset elements of pilot/driver information displayed in the viewing     device D_(v) are superposed or aligned with one or more     corresponding landmarks of the real outside world the theoretical     rotation matrices Û_(i) of which in the exterior reference     coordinate system are known; then -   in a second step, and using a dual harmonization algorithm,     conjointly calculating the relative orientation matrix {circumflex     over (R)}(S1/v) of the tracking first element S1 of the     posture-detecting subsystem with respect to the viewing device D_(v)     and/or the relative orientation matrix {circumflex over (R)}(ref/S2)     of the external reference device D_(Ref) with respect to the fixed     solid second element S2 of the posture-detecting subsystem to     respectively be the right-side bias rotation matrix {circumflex over     (D)} and the left-side bias rotation matrix Ĝ, which are conjoint     solutions of the system of dual harmonization equations:     Û_(i)=Ĝ·{circumflex over (K)}_(i)·{circumflex over (D)}, i varying     from 1 to N.

According to particular embodiments, the method for dual harmonization of a DDP posture-detecting subsystem includes one or more of the following features implemented alone or in combination:

-   the minimum required number N of measurements depends on the number     L of erroneous or inexploitable degrees of angular freedom of the     rotation matrices {circumflex over (R)}(S1/v) and R(ref/S2) of the     head-up viewing system, said number L being an integer higher than     or equal to 1 and lower than or equal to 6, and the solution of the     system of equations Û_(i)=Ĝ·{circumflex over (K)}_(i)·{circumflex     over (D)}, i varying from 1 to N, uses a rectification operator π(.)     that converts any given matrix A into a 3×3 square rotation matrix     π(A), which matrix π(A), of all the 3×3 rotation matrices, is the     closest in the least-squares sense to all of the terms of the matrix     π(A) A, to determine the right-side rotation {circumflex over (D)}     and the left-side rotation Ĝ;

in a first configuration, the number of erroneous or inexploitable degrees of angular freedom of the right-side bias rotation matrix {circumflex over (D)} is equal to three and the number of erroneous or inexploitable degrees of angular freedom of the left-side bias rotation matrix Ĝ is equal to three, the first step carries out a number N higher than or equal to 3 of measurements, for which measurements the targeting actions Vi correspond to an alignment of displayed three-dimensional reference marks with observed exterior three-dimensional reference marks, and the second step of solving the system of dual harmonization equations comprises a first set of substeps consisting in: in a first substep, choosing a “pivot” measurement as the first measurement among the N measurements, this pivot measurement corresponding to i equal to 1, and for i=2, , N the rotation matrices Û_(1,i) and {circumflex over (K)}_(1,i) are calculated using the equations: Û_(1,i)=Û₁ ^(T)·Û_(i) and {circumflex over (K)}_(1,i)={circumflex over (K)}₁ ^(T)·{circumflex over (K)}_(i); then in a second substep, determining for i=2, . . . , N the principle unit vectors of the rotations Û_(1,i) and {circumflex over (K)}_(1,i), designated by {right arrow over (u)}_(i) and {right arrow over (k)}_(i), respectively; then in a third substep, calculating the right matrix {circumflex over (D)} using the equation: {circumflex over (D)}=π(Σ_(i≥2)({right arrow over (k)}_(i)·{right arrow over (u)}_(i) ^(T))); then in a fourth substep, determining the left-side rotation matrix Ĝ on the basis of the matrix {circumflex over (D)} calculated in the third substep, using the equation:

$\hat{G} = {\pi\left( {\sum\limits_{i \geq 1}\left( {{\hat{U}}_{i} \cdot {\hat{D}}^{T} \cdot {\hat{K}}_{i}^{T}} \right)} \right)}$

-   in a second configuration, the number of erroneous or inexploitable     degrees of angular freedom of the right-side bias rotation matrix     {circumflex over (D)} is equal to three and the single erroneous or     inexploitable degree of angular freedom of the left-side bias     rotation matrix Ĝ is the azimuth angle, the elevation and roll     angles being assumed to be known with a sufficient precision; the     first step carries out a number N higher than or equal to 4 of     measurements, for which measurements the targeting actions Vi     correspond to an alignment of displayed three-dimensional reference     marks with observed three-dimensional reference marks; and the     second step of solving the system of dual harmonization equations     comprises a second set of substeps consisting in: in a fourth     substep for i=2, . . . ,N, calculating the matrices Û_(1,i) and the     vectors {right arrow over (q)}_(i) using the equations: Û_(1,i)=Û₁     ^(t)·Û_(i) and {right arrow over (q)}_(i)={circumflex over (Q)}_(i)     ^(T)·{right arrow over (k)}, the vector {right arrow over (k)} being     defined by the equation

${\overset{\rightarrow}{k} = \begin{pmatrix} 0 \\ 0 \\ 1 \end{pmatrix}};$

then in an initialization fifth substep, initializing a first sequence of matrices {{circumflex over (D)}_([s])}, [s] designating the current integer rank of advancement through the sequence {{circumflex over (D)}_([s])}, by setting {circumflex over (D)}_([0]) equal to I₃, I₃ being the identity matrix; then repeating an iterative sixth substep in which iteration [s+1] is passed to from iteration [s] by calculating the vector value {right arrow over (d)}_([s+1]), then the value {circumflex over (D)}_([s+1]) of the first matrix sequence {{circumflex over (D)}_([s])}, using the following equations:

${\overset{\rightarrow}{d}}_{\lbrack{s + 1}\rbrack} = \frac{\sum_{i \geq 2}\left( {{\hat{U}}_{1,i} \cdot {\hat{D}}_{\lbrack s\rbrack}^{T} \cdot {\overset{\rightarrow}{q}}_{i}} \right)}{{\sum_{i \geq 2}\left( {{\hat{U}}_{1,i} \cdot {\hat{D}}^{T} \cdot {\overset{\rightarrow}{q}}_{i}} \right)}}$ ${\hat{D}}_{\lbrack{s + 1}\rbrack} = {\pi\left( {\sum\limits_{i \geq 2}\left( {{\overset{\rightarrow}{q}}_{i} \cdot {\overset{\rightarrow}{d}}_{\lbrack{s + 1}\rbrack}^{T} \cdot {\hat{U}}_{1,i}} \right)} \right)}$

the sequence {{right arrow over (d)}_([s])} being an auxiliary second sequence of vectors and the sequence {{circumflex over (D)}_([s])} converging to {circumflex over (D)}; and stopping in a seventh substep the iterative process carried out throughout the sixth substep when the limit {circumflex over (D)} is approximated with a sufficient precision defined by a preset threshold value;

in a third configuration, the number of erroneous or inexploitable degrees of angular freedom of the right-side bias rotation matrix {circumflex over (D)} is equal to three and the number of erroneous or inexploitable degrees of angular freedom of the left-side bias rotation matrix Ĝ is equal to three; and the first step carries out a number N higher than or equal to 4 of measurements, for which measurements the targeting actions Vi correspond to an alignment of a plurality of different targeting directions {right arrow over (x)}_(i) with a plurality of targeted exterior directions {right arrow over (y_(l))} that are known in the reference exterior coordinate system R_(Ref), without roll adjustment, the vector families {{right arrow over (x)}_(i)} and {{right arrow over (y)}_(i)} both being free; and the second step of solving the system of dual harmonization equations: {right arrow over (y)}_(i)=Ĝ·{circumflex over (K)}_(i)·{circumflex over (D)}·{right arrow over (x)}_(i) for i varying from 1 to N comprises a third set of the following substeps consisting in: in an initialization eighth substep, initializing a first sequence of left matrices {Ĝ_([s])}, [s] designating the integer rank of advancement through this first sequence, by setting Ĝ_([0]) equal to I₃, I₃ being the identity matrix; then repeating an iterative ninth substep in which iteration [s+1] is passed to from iteration [s] by calculating the matrix {circumflex over (D)}_([s+1]) then the matrix Ĝ_([s+1]) using the following equations:

${\hat{D}}_{\lbrack{s + 1}\rbrack} = {\pi\left( {\sum\limits_{i \geq 1}\left( {{\hat{K}}_{i}^{T} \cdot {\hat{G}}_{\lbrack s\rbrack}^{T} \cdot {\overset{\rightarrow}{y}}_{i} \cdot {\overset{\rightarrow}{x}}_{i}^{T}} \right)} \right)}$ ${\hat{G}}_{\lbrack{s + 1}\rbrack} = {\pi\left( {\sum\limits_{i \geq 1}\left( {{\overset{\rightarrow}{y}}_{i} \cdot {\overset{\rightarrow}{x}}_{i}^{T} \cdot {\hat{D}}_{\lbrack{s + 1}\rbrack}^{T} \cdot {\hat{K}}_{i}^{T}} \right)} \right)}$

the sequence {{circumflex over (D)}_([s])} being a second sequence of right matrices, and the sequences {circumflex over (D)}_([s]) and Ĝ_([s]) converging to {circumflex over (D)} and Ĝ, respectively; and stopping in a stopping tenth substep the iterative process executed throughout the ninth substep when the limits {circumflex over (D)} and Ĝ are approximated with a sufficient precision;

in a fourth configuration, the number of erroneous or inexploitable degrees of angular freedom of the right-side bias rotation matrix {circumflex over (D)} is equal to three and the left-side bias rotation matrix Ĝ is assumed known; and the first step carries out a number N higher than or equal to 3 of measurements, for which measurements the targeting actions Vi correspond to an alignment of N different targeting directions {right arrow over (x)}_(i) with one and the same targeted exterior direction {right arrow over (y₀)}, which targeted direction is known in the reference exterior coordinate system R_(Ref), without roll adjustment, the vector family {{right arrow over (x)}_(i)} being free; and the second step of solving the system of dual harmonization equations: Ĝ·{circumflex over (K)}_(i)·{circumflex over (D)}·{right arrow over (x)}_(i)={right arrow over (y)}₀ for i varying from 1 to N determines the right bias rotation matrix {circumflex over (D)} via the following equation:

{circumflex over (D)}=π(Σ_(i>1)({circumflex over (K)} _(i) ^(T) ·Ĝ ^(T) ·{right arrow over (y)} ₀ ·{right arrow over (x)} _(i) ^(T)));

in a fifth configuration, the number of erroneous or inexploitable degrees of angular freedom of the right-side bias rotation matrix {circumflex over (D)} is equal to three and the left-side bias rotation matrix Ĝ is assumed to be known; and the first step carries out a number N higher than or equal to 4 of measurements, for which measurements the targeting actions Vi correspond to an alignment of N different targeting directions {right arrow over (x)}_(i) with one and the same unknown targeted exterior direction {right arrow over (y₀)}, without roll adjustment, the vector family {{right arrow over (x)}_(i)} being free; and the second step of solving the system of dual harmonization equations: Ĝ·{circumflex over (K)}_(i)·{circumflex over (D)}·{right arrow over (x)}_(i)={right arrow over (y)}₀ for i varying from 1 to N comprises a fifth set of substeps consisting in: in an initialization eleventh substep, initializing a first sequence of right matrices {{circumflex over (D)}_([s])}, [s] designating the integer rank of advancement through the sequence {{circumflex over (D)}_([s])}, by setting {circumflex over (D)}_([0]) equal to I₃, I₃ being the identity matrix; then repeating an iterative twelfth substep in which iteration [s+1] is passed to from iteration [s] by calculating the vector {right arrow over (y)}_([s+1]) then the matrix {circumflex over (D)}_([s+1]) using the following equations:

${\overset{\rightarrow}{y}}_{\lbrack{s + 1}\rbrack} = \frac{\sum_{i \geq 1}\left( {\hat{G} \cdot {\hat{K}}_{i} \cdot {\hat{D}}_{\lbrack s\rbrack} \cdot {\overset{\rightarrow}{x}}_{i}} \right)}{{\sum_{i \geq 1}\left( {\hat{G} \cdot {\hat{K}}_{i} \cdot {\hat{D}}_{\lbrack s\rbrack} \cdot {\overset{\rightarrow}{x}}_{i}} \right)}}$ ${\hat{D}}_{\lbrack{s + 1}\rbrack} = {\pi\left( {\sum\limits_{i \geq 1}\left( {{\hat{K}}_{i}^{T} \cdot {\hat{G}}^{T} \cdot {\overset{\rightarrow}{y}}_{\lbrack{s + 1}\rbrack} \cdot {\overset{\rightarrow}{x}}_{i}^{T}} \right)} \right)}$

the sequence {{right arrow over (y)}_([s])} being a second sequence of external direction vectors, and the sequences {{right arrow over (y)}_([s])} and {{circumflex over (D)}_([s])} converging to {right arrow over (y₀)} and {circumflex over (D)}, respectively; and stopping in a stopping thirteenth substep the iterative process carried out throughout the twelfth substep when the limits {right arrow over (y₀)} and {circumflex over (D)} are approximated with a sufficient precision defined by one or two preset threshold values;

in a sixth configuration, the number of erroneous or inexploitable degrees of angular freedom of the right-side bias rotation matrix {circumflex over (D)} is equal to three and the left-side bias rotation matrix Ĝ is unknown and indeterminable; and the first step carries out a number N higher than or equal to 4 of measurements, for which measurements the targeting actions Vi correspond to an alignment of N different targeting directions {right arrow over (x)}_(i) with one and the same unknown targeted exterior direction {right arrow over (y₀)}, without roll adjustment, the vector family {{right arrow over (x)}_(i)} being free, and reduces the solution of the system of dual harmonization equations: Ĝ·{circumflex over (K)}_(i)·{circumflex over (D)}·{right arrow over (x)}_(i)={right arrow over (y)}₀ for i varying from 1 to N to the solution of the reduced system of dual harmonization equations: {circumflex over (K)}_(i)·{circumflex over (D)}·{right arrow over (x)}_(i)={right arrow over (z)}₀ for i varying from 1 to 4, noting {right arrow over (z)}₀=Ĝ^(T)·{right arrow over (y)}₀; and the second step of solving the reduced system of dual harmonization equations comprises a sixth set of substeps consisting in: in an initialization fourteenth substep, initializing a first sequence of right matrices {{circumflex over (D)}_([s])}, [s] designating the integer rank of advancement through the sequence {{circumflex over (D)}_([s])}, by setting {circle around (D)}_([0]) equal to I₃, I₃ being the identity matrix; then repeating an iterative fifteenth substep in which iteration [s+1] is passed to from iteration [s] by calculating the vector {right arrow over (z)}_([s+1]) then the matrix {circumflex over (D)}_([s+1]) of the first matrix sequence using the following equations:

${\overset{\rightarrow}{z}}_{\lbrack{s + 1}\rbrack} = \frac{\sum_{i \geq 1}\left( {{\hat{K}}_{i} \cdot {\hat{D}}_{\lbrack s\rbrack} \cdot {\overset{\rightarrow}{x}}_{i}} \right)}{{\sum_{i \geq 1}\left( {{\hat{K}}_{i} \cdot {\hat{D}}_{\lbrack s\rbrack} \cdot {\overset{\rightarrow}{x}}_{i}} \right)}}$ ${\hat{D}}_{\lbrack{s + 1}\rbrack} = {\pi\left( {\sum\limits_{i \geq 1}\left( {{\hat{K}}_{i}^{T} \cdot {\overset{\rightarrow}{z}}_{\lbrack{s + 1}\rbrack} \cdot {\overset{\rightarrow}{x}}_{i}^{T}} \right)} \right)}$

the sequence {{right arrow over (z)}_([s])} being a second auxiliary sequence of vectors and the sequence {{circumflex over (D)}_([s])} converging to {circumflex over (D)}; and stopping in a stopping sixteenth substep the iterative process carried out throughout the fifteenth substep when the limit {circumflex over (D)} is approximated with a sufficient precision defined by a preset threshold value;

In a seventh configuration, the number of erroneous or inexploitable degrees of angular freedom of the left-side bias rotation matrix Ĝ is equal to three and the right-side bias rotation matrix {circumflex over (D)} is assumed to be known; and the first step carries out a number N higher than or equal to 3 of measurements, for which measurements the targeting actions Vi correspond to an alignment of one and the same known targeting direction {right arrow over (x)}₀ with N known targeted exterior directions {right arrow over (y_(l))}, without roll adjustment, the vector family {{right arrow over (y)}_(i)} being free, and the second step of solving the system of dual harmonization equations: Ĝ·{circumflex over (K)}_(i)·{circumflex over (D)}·{right arrow over (x)}₀={right arrow over (y)}_(i) for i varying from 1 to N determines the sought left rotation matrix Ĝ using the equation: Ĝ=π(Σ_(i≥1)({right arrow over (y)}_(i)·{right arrow over (x)}₀ ^(T)·{circumflex over (D)}^(T)·{circumflex over (K)}_(i) ^(T)));

in an eighth configuration, the number of erroneous or inexploitable degrees of angular freedom of the left-side bias rotation matrix Ĝ is equal to three and the right-side bias rotation matrix {circumflex over (D)} is assumed to be known; and the first step carries out a number N higher than or equal to 4 of measurements, for which measurements the targeting actions Vi correspond to an alignment of one and the same unknown targeting direction {right arrow over (x)}₀ with N known targeted exterior directions {right arrow over (y_(l))}, without roll adjustment, the vector family {{right arrow over (y)}_(i)} being free; and the second step of solving the system of dual harmonization equations: Ĝ·{circumflex over (K)}_(i)·{circumflex over (D)}·{right arrow over (x)}₀={right arrow over (y)}_(i) for i varying from 1 to N comprises an eighth set of substeps consisting in: in a seventeenth substep, initializing a first sequence of left matrices {Ĝ_([s])}, [s] designating the integer rank of advancement through the sequence {Ĝ_([s])}, Ĝ_([0]) being initialized set equal to I₃, I₃ being the identity matrix; then repeating an iterative eighteenth substep in which iteration [s+1] is passed to from iteration [s] by calculating the vector {right arrow over (x)}_([s+1]) then the matrix Ĝ_([s+1]) using the following equations:

${\overset{\rightarrow}{x}}_{\lbrack{s + 1}\rbrack} = \frac{\sum_{i \geq 1}\left( {{\hat{D}}^{T} \cdot {\hat{K}}_{i}^{T} \cdot {\hat{G}}_{\lbrack s\rbrack}^{T} \cdot {\overset{\rightarrow}{y}}_{i}} \right)}{{\sum_{i \geq 1}\left( {{\hat{D}}^{T} \cdot {\hat{K}}_{i}^{T} \cdot {\hat{G}}_{\lbrack s\rbrack}^{T} \cdot {\overset{\rightarrow}{y}}_{i}} \right)}}$ ${\hat{G}}_{\lbrack{s + 1}\rbrack} = {\pi\left( {\sum\limits_{i \geq 1}\left( {{\overset{\rightarrow}{y}}_{i} \cdot {\overset{\rightarrow}{x}}_{\lbrack{s + 1}\rbrack}^{T} \cdot {\hat{D}}^{T} \cdot {\hat{K}}_{i}^{T}} \right)} \right)}$

the sequence {{right arrow over (x)}_([s])} being a second sequence of targeting direction vectors, the sequences Ĝ_([s]) and {right arrow over (x)}_([s]) converging to Ĝ and {right arrow over (x)}₀, respectively; and in a stopping nineteenth substep stopping the iterative process carried out throughout the eighteenth substep when the limits Ĝ and optionally {right arrow over (x)}₀ are approximated with a sufficient precision defined by one or two preset threshold values;

the head-up viewing system is intended to be located on-board a carrier vehicle comprised in the set of all aircraft, aeroplanes, helicopters, motor vehicles and robots.

Another subject of the invention is a worn/borne head-up viewing system located on-board a carrier vehicle and comprising: a transparent worn/borne head-up viewing device D_(v), a reference device D_(ref) having a reference coordinate system R_(ref), possibly either a coordinate system of the carrier vehicle or a local geographic coordinate system or a terrestrial coordinate system; a DDP posture-detecting subsystem comprising a tracking solid first element S1 rigidly and tightly attached to the viewing device D_(v), a fixed solid second element S2 tightly joined to the reference device D_(ref), and a means for measuring and determining the relative orientation {circumflex over (K)} of the tracking mobile first element S1 with respect to the fixed second element S2; a dual harmonization subsystem for harmonizing the head-up viewing system and the DDP posture-detecting subsystem, the dual harmonization subsystem comprising a dual harmonization processor and an HMI interface for managing the acquisitions of the harmonization measurements.

The worn/borne head-up viewing system is characterized in that the dual harmonization subsystem and the DDP posture-detecting subsystem are configured to:

in a first step, carry out a series of a preset number N of measurements of relative orientations {circumflex over (K)}_(l), i varying from 1 to N, of the tracking mobile first element S1 with respect to the fixed second element S2 of the DDP posture-detecting subsystem, corresponding to different targeting actions Vi, i varying from 1 to N, in which measurements one or more different preset elements of pilot/driver information displayed in the viewing device D_(v) are superposed or aligned with one or more corresponding landmarks of the real outside world; then i

n a second step, and using a dual harmonization algorithm, conjointly calculate the relative orientation matrix {circumflex over (R)}(S1/v) of the tracking first element S1 of the posture-detecting subsystem with respect to the viewing device D_(v) and/or the relative orientation matrix {circumflex over (R)}(ref/S2) of the external reference device D_(Ref) with respect to the fixed solid second element S2 of the posture-detecting subsystem to respectively be the right-side bias rotation matrix {circumflex over (D)} and the left-side bias rotation matrix Ĝ, which are conjoint solutions of the system of dual harmonization equations: Û_(i)=Ĝ·{circumflex over (K)}_(i)·{circumflex over (D)}, i varying from 1 to N.

According to particular embodiments, the head-up viewing system includes one or more of the following features implemented alone or in combination:

the minimum required number N of measurements depends on the number L of erroneous or inexploitable degrees of angular freedom of the rotation matrices {circumflex over (R)}(S1/v) and {circumflex over (R)}(ref/S2) of the head-up viewing system, said number L being an integer higher than or equal to 1 and lower than or equal to 6, and the solution of the system of equations Û_(i)=Ĝ·{circumflex over (K)}_(i)·{circumflex over (D)}, i varying from 1 to N, uses a rectification operator π(.) that converts any given matrix A into a 3×3 square rotation matrix π(A), which matrix π(A), of all the 3×3 rotation matrices, is the closest in the least-squares sense to all of the terms of the matrix π(A)−A, to determine the right-side rotation {circumflex over (D)} and the left-side rotation Ĝ.

the dual harmonization subsystem and the DDP posture-detecting subsystem are configured to implement the first and second steps such as defined above.

Another subject of the invention is a carrier vehicle, comprised in the set of all aircraft, aeroplanes, helicopters, motor vehicles and robots, and in which is installed a worn/borne head-up viewing system such as defined above.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will be better understood on reading the following description of a plurality of embodiments, which is given merely by way of example and which makes reference to the drawings, in which:

FIG. 1 is a general view of a worn head-up viewing system according to the invention allowing dual harmonization of the posture-detecting subsystem that is a constituent of said head-up viewing system;

FIG. 2 is a general flowchart of a method for dual harmonization of the posture-detecting subsystem integrated into the worn head-up viewing system;

FIG. 3 is a flowchart of a first particular embodiment of a dual harmonization method according to the invention;

FIG. 4 is a flowchart of a second particular embodiment of a dual harmonization method according to the invention;

FIG. 5 is a flowchart of a third particular embodiment of a dual harmonization method according to the invention;

FIG. 6 is a flowchart of a fourth particular embodiment of a dual harmonization method according to the invention;

FIG. 7 is a flowchart of a fifth particular embodiment of a dual harmonization method according to the invention;

FIG. 8 is a flowchart of a sixth particular embodiment of a dual harmonization method according to the invention;

FIG. 9 is a flowchart of a seventh particular embodiment of a dual harmonization method according to the invention;

FIG. 10 is a flowchart of an eighth particular embodiment of a dual harmonization method according to the invention.

DETAILED DESCRIPTION

According to FIG. 1, a head-up viewing system 2 according to the invention, which system is intended to be located on-board a mobile carrier vehicle, for example an aircraft, comprises the following devices and means:

a transparent worn head-up viewing or displaying device 12, a lens for example, designated by D_(v), that is positioned in front of the eye of a pilot and able to serve him as a sight;

a reference device 14, designated by D_(ref), having a reference coordinate system, designated by R_(ref), which may be either a coordinate system of the carrier vehicle, or a local geographic coordinate system, or a terrestrial coordinate system;

a DDP posture-detecting subsystem 16 comprising:

a tracking angularly mobile solid first element 18 S1, which is rigidly attached to the head or helmet of the pilot, and tightly or rigidly attached to the viewing device 12 D_(v),

a fixed solid second element 20 S2, which is tightly linked to the reference device 14 D_(ref), and

a means 26 for measuring and determining the relative orientation {circumflex over (R)}(R_(S2)/R_(S1)) of the tracking mobile first element 18 S1 with respect to the fixed second element 22 S2, which is tightly linked to the reference device 14 D_(ref), the relative orientation also being denoted {circumflex over (R)}(R_(S2)/R_(S1)),

a dual harmonization subsystem 32 for harmonizing the components of the head-up viewing system 2 and the DDP posture-detecting subsystem 16, the dual harmonization subsystem 32 comprising a dual harmonization processor 34 and a human-system interface 38, which is configured to perform and manage interfacing operations between the operator or the pilot and the components of the head-up viewing system 2 during the implementation of the dual harmonization method according to the invention.

Below, a coordinate system denoted “R_(i)” will, for the sake of simplicity, be denoted “i”.

Below, the rotation-matrix notation “{circumflex over (R)}(R_(i)/R_(j))” will be simplified to the notation “{circumflex over (R)}(i/j)”. Thus, for example, the matrix {circumflex over (R)}(R_(S2)/R_(S1)) will be more simply denoted the matrix {circumflex over (R)}(S2/S1).

Below, the means allowing the relative orientation of a coordinate system “i” with respect to another “j” to be known are considered equivalent in the rest of this document to the matrix describing this orientation. Specifically, the orientation {circumflex over (R)}(i/j) of a coordinate system “i” with respect to another “j” may be described either by:

three what are called Euler angles, which conventionally, in aeronautics, correspond to the order of the rotations for the following angles:

Azimuth: rotation about the z-axis, which is oriented downward (or toward the Earth);

Elevation: rotation about the y-axis, which is oriented toward the right (or toward the east of the Earth);

Roll: rotation about the x-axis, which is oriented frontward (or toward the north of the Earth),

or a 3×3 matrix describing this rotation.

The matrix {circumflex over (R)}(i/j) describing the relative orientation of the coordinate system “i” with respect to “j” (or from “i” to “j”) allows the expression vi of a vector in the coordinate system “i” to be related to the expression vj of the same vector in the coordinate system “j” by the relationship: vi=M(i/j)*vj and the relationship of passage between the coordinate systems “i”, “j”, and “k” is written: {circumflex over (R)}(i/k)={circumflex over (R)}(j/k)*{circumflex over (R)}(i/j).

The tight link between the tracking mobile solid first element S1 18 of the DDP posture-detecting subsystem 16 and the targeting and viewing device 12 D_(v) is a first link 42 that is assumed to be rigid, and which ensures that the rotation matrix {circumflex over (R)}(S1/v) allowing the passage from the first orthonormal coordinate system R_(S1) attached to the orientable solid first element S1 of the DDP posture-detecting subsystem 16 to the targeting and viewing coordinate system R_(v) is a rotation matrix that is invariant in time.

The tight link between the solid second element 20 S2 of the DDP posture-detecting subsystem 16 and the fixed reference device 14 D_(ref) is a second rigid link that ensures that the rotation matrix {circumflex over (R)}(Ref/S2) allowing the passage from the fixed coordinate system R_(ref) to the second orthonormal coordinate system R_(S2) attached to the fixed solid second element S2 of the DDP posture-detecting subsystem 16 is a rotation matrix that is invariant in time.

Generally, the fixed reference coordinate system R_(ref) is the coordinate system in which the coordinates of objects that it is desired to observe in the viewing and aligning coordinate system R_(v) linked to the viewing and targeting device 12 D_(v) are known. The DDP posture-detecting subsystem 16 then allows the real or virtual objects of the reference coordinate system to be “projected” into the viewing coordinate system. In particular, if the viewing device 12 D_(v) is transparent, it is possible to superpose the projected objects on their real image, conformal projection then being spoken of.

In any case, the useful output information DDP_(useful) that it is sought to deliver to the pilot or to the piloting device, i.e. the rotation between the coordinate system R_(v) of the sight of the helmet of the pilot and the reference coordinate system R_(ref) is different from the raw output DDP_(raw) calculated by the DDP posture-detecting system, i.e. the measured and calculated rotation matrix between the first orthonormal coordinate system R_(S1), which is tightly linked via the first link 42 to the targeting and viewing coordinate system R_(v), and the second orthonormal coordinate system R_(S2) , which is tightly linked via the second link 44 to the reference coordinate system R_(ref).

The useful information DDP_(useful) that it is sought to deliver to the pilot or to the piloting device and the raw output DDP_(raw) calculated by the DDP posture-detecting subsystem are then related by the relationship:

DDP _(useful) ={circumflex over (R)}(Ref/S2)*DDP _(raw) *{circumflex over (R)}(S1/v)

deduced from the relationship:

R(Ref/v)={circumflex over (R)}(Ref/S2)*{circumflex over (R)}(S2/S1)*R(S1/v)

In the dual harmonization method of the invention, it is assumed that the left-side and right-side error matrices, {circumflex over (R)}(Ref/S2) and {circumflex over (R)}(S1/v), are matrices that are invariant in time and rotation matrices.

The determination of these left and right error matrices {circumflex over (R)}(Ref/S2) and {circumflex over (R)}(S1/v) is made possible by:

the provision of a number N of orientation measurements DDP_(raw) carried out by the posture-detecting system, corresponding to various measurement stations, i.e. different targeting or pointing directions, using one or more different virtual or real landmarks the attitudes of which are known in the reference coordinate system, and the real rotation matrices DDP_(useful),

algorithms for solving a system of dual harmonization equations:

DDP _(useful)(i)=Ĝ·DDP _(raw)(i)·{circumflex over (D)}, i varying from 1 to N.

These algorithms are based on a mathematical method allowing any given (and in practice invertible) matrix A to be “rectified” into a rotation matrix.

The rectification consists in finding, in the set of all of the rotation matrices, the rotation matrix π(A) that is the closest to the matrix A in the least-squares sense, i.e. to all of the terms of said matrix A. π(A) is called the rectified form of A and π(.) is the rectification operator.

The head-up viewing system is configured, by way of the dual harmonization subsystem 16 in particular, to implement all of the embodiments described below of the dual harmonization method according to the invention.

According to FIG. 2 and generally, a method 52 for dual harmonization of the DDP posture-detecting subsystem 16 integrated into the head-up viewing system 2 or of any output rotation matrix measured and calculated by the detecting subsystem comprises a first step 54 and a second step 56, which are executed in succession.

In the first step 54 of measurement acquisition, a number N of orientation measurements or output matrices DDP_(raw)(i), denoted {circumflex over (K)}_(i) below, i varying from 1 to N and being an index of identification of each measurement, are acquired.

The measurements of the matrices {circumflex over (K)}_(i), i varying from 1 to N, correspond to various measurement stations or to different targeting actions Vi using one or more different real landmarks, and the expected useful DDP value DDP_(useful)(l), designated Û_(i) below, of which is theoretically known.

For each measurement station or targeting action Vi, the output rotation value {circumflex over (K)}_(i) calculated by the DDP posture-detecting subsystem 16, and the expected useful rotation value Û_(i) are related by the constitutive relationship of the harmonized system: Û_(i)=Ĝ·{circumflex over (K)}_(i)·{circumflex over (D)}.

In the second step 56, the left and right bias matrices G and {circumflex over (D)}, which are invariant in time, are determined conjointly by solving the system of dual harmonization equations:

Û _(i) =Ĝ·{circumflex over (K)} _(i) ·{circumflex over (D)}, i varying from 1 to N.

What should be noted is that, in any way, not described in detail here, knowledge is obtained firstly of a certain number of measurements, which are completely defined by three vectors or a three-dimensional matrix, or only partially defined, a number of matrix coefficients strictly lower than 9 then being partially defined, and secondly of theoretical values that are associated with the corresponding measurement stations, these values also being completely or partially known.

Thus, for each measurement station or targeting action Vi all or some of the three degrees of freedom of {circumflex over (K)}_(i), and all or some of the three degrees of freedom of Û_(i) are acquired.

The measurements, nominally consisting in the rotation matrix delivered by the DDP subsystem, therefore contain three delivered degrees of freedom. In practice, the DDP subsystem may deliver only two, or even only a single degree of freedom of the solution allows to solve even if the number of measurement stations increases.

The π rectifying technique used by the global harmonization method according to the invention allows, provided that a sufficient number of measurements are acquired, i.e. a number such that from a mathematical point of view the rank of the system of equations is sufficient, the unknown rotation matrices Ĝ and {circumflex over (D)}to be determined.

The dual harmonization method, because of the rectification technique used, is based on three particular mathematical tools, designated O1, O2 and O3, that, alone or in combination, allow each and every soluble measuring-station configuration to be solved.

According to the first tool O1, when a sequence of rotation matrices, designated by {{circumflex over (R)}_(i)}, and a sequence of normalized vectors, designated by {{right arrow over (e)}_(i)}, are given such that the product {circumflex over (R)}_(i)·{right arrow over (e)}_(i) is a constant vector, then the best value of this constant vector {right arrow over (e)}_(i) is given by:

$\overset{\rightarrow}{e} = \frac{\sum_{i}\left( {{\hat{R}}_{i} \cdot {\overset{\rightarrow}{e}}_{i}} \right)}{{\sum_{i}\left( {{\hat{R}}_{i} \cdot {\overset{\rightarrow}{e}}_{i}} \right)}}$

To be able to use the first tool O1, the required minimum number of measurement configurations allowing the harmonization problem to be solved is equal to 1 provided that the mathematical constraint:

${\sum\limits_{i}\left( {{\hat{R}}_{i} \cdot {\overset{\rightarrow}{e}}_{i}} \right)} \neq \overset{\rightarrow}{0}$

is met.

According to the second tool O2, when two sequences of vectors {{right arrow over (a)}_(i)} and {{right arrow over (b)}_(i)} are given such that the second sequence is an image of the first sequence found by applying a constant rotation {circumflex over (R)}, then the best value of this constant rotation is defined by the equation:

$\hat{R} = {\pi\left( {\sum\limits_{i}\left( {{\overset{\rightarrow}{b}}_{i} \cdot {\overset{\rightarrow}{a}}_{i}^{T}} \right)} \right)}$

in which (.)^(T) is the transposition operator.

To be able to use the second tool O2, the required minimum number of measurement configurations allowing the harmonization problem to be solved is equal to 2 provided that each of the two families or sequences of vectors {{right arrow over (a)}_(i)} and {{right arrow over (b)}_(i)} is free.

According to the third tool O3, when a sequence of rotation matrices {{circumflex over (R)}_(i)} that are mathematically equal to a constant rotation is given, then the best value of this rotation is defined by the equation:

$\hat{R} = {\pi\left( {\sum\limits_{i}{\hat{R}}_{i}} \right)}$

To be able to use the third tool O3, the required minimum number of measurement configurations allowing the harmonization problem to be solved is Σ_(i){circumflex over (R)}_(i) is not a zero matrix, is met.

In FIG. 3, and in a nominal configuration forming a first harmonization-method configuration 102, a preset number N of raw DDP rotation-matrix measurements {circumflex over (K)}_(i) are carried out in a first step 104, each measurement {circumflex over (K)}_(i) being identified by its advancement index “i”, which is comprised between 1 and N.

Each measurement “i” corresponds to a different measurement station in which a first three-dimensional 3D reference mark of the pointing device or targeting device, for example corresponding to a reticle, is aligned with a second three-dimensional 3D reference mark of an external object that is fixed with respect to the fixed coordinate system R_(ref), and therefore one taking account of the three degrees of freedom. For example, a known or preset posture of the helmet of the pilot is captured by an exterior means, for example a robot or a video observation camera, which means is coupled to a means for collecting the output for a rotation with respect to a reference coordinate system, corresponding to an alignment of a three-dimensional 3D image of known position in the coordinate system of the sight of the helmet and a preset real external landscape of known position in the fixed reference coordinate system R_(ref).

It is assumed here that for the sequence of N measurements identified by the index “i” varying from 1 to N, i.e. the calculated rotation matrices {circumflex over (K)}_(i), the corresponding theoretical matrices Û_(i) are entirely known.

In this case, and according to the dual harmonization method of the invention, it is necessary to solve the following system of equations:

Û _(i) =Ĝ·{circumflex over (K)} _(i) ·{circumflex over (D)}

with i varying from 1 to N.

In a second step 106, the system of equations that was described above is reduced and solved by implementing a first set 112 of first, second and third substeps 114, 116, 118.

In a first substep 114, a “pivot” measurement is chosen, for example the first measurement corresponding to i equal to 1.

It is then possible to verify that for i=2, . . . , N: Û₁ ^(T)·Û_(i)={circumflex over (D)}^(T)·{circumflex over (K)}₁ ^(T)·{circumflex over (K)}_(i)·{circumflex over (D)}.

Thus, noting Û_(1,i)=Û₁ ^(T)·_(i) and {circumflex over (K)}_(1,i)={circumflex over (K)}₁ ^(T)·K_(i), it is possible to write: {circumflex over (D)}·Û_(1,i)={circumflex over (K)}_(1,i)·{circumflex over (D)}.

In the first substep 114, the rotation matrices Û_(1,i) and {circumflex over (K)}_(1,i) are thus calculated for i=2, . . . , N using the equations: Û_(1,i)=Û₁ ^(T)·Û_(i) and {circumflex over (K)}_(1,i)={circumflex over (K)}₁ ^(T)·{circumflex over (K)}_(i).

Next, in a second substep 116, the reduction of the system of equations: Û_(i)=Ĝ·{circumflex over (K)}_(i)·{circumflex over (D)}, i varying from 1 to N, is completed using the fact that the latter equations are mathematically equivalent to: {circumflex over (D)}·{right arrow over (u)}_(i)={right arrow over (k)}_(i), where {right arrow over (u)}_(i) and {right arrow over (k)}_(i) are respectively the principal unit vectors of the rotations Û_(1,i) and {circumflex over (K)}_(1,i).

Thus, in the second substep 116, the principal unit vectors of the rotations Û_(1,i) and {circumflex over (K)}_(1,i), which vectors are designated {right arrow over (u)}_(i) and {right arrow over (k)}_(i), respectively, are determined in a known way for i=2, . . . , N.

Next, in a third substep 118, the right matrix {circumflex over (D)} is calculated using the equation:

$\hat{D} = {\pi\left( {\sum\limits_{i \geq 2}\left( {{\overset{\rightarrow}{k}}_{i} \cdot {\overset{\rightarrow}{u}}_{i}^{T}} \right)} \right)}$

in which π(.) is a rectification or projection operator that converts any given matrix A into the 3×3 square rotation matrix π(A) that is, of all 3×3 rotation matrices, the closest, in the least-squares sense, to all of the terms of the matrix π(A)−A.

Next, in a fourth substep 120, the left-side rotation matrix Ĝ is determined on the basis of the matrix {circumflex over (D)}, which was calculated in the third substep 118, using the equation:

$\hat{G} = {\pi\left( {\sum\limits_{i \geq 1}\left( {{\hat{U}}_{i} \cdot {\hat{D}}^{T} \cdot {\hat{K}}_{i}^{T}} \right)} \right)}$

It will be noted that mathematical study of the projection π shows that the choice of the pivot among the N measurements is without influence on the final result of the harmonization.

It will also be noted that mathematical study of the projection π shows that the choice as to whether to determine {circumflex over (D)} or Ĝ first is also without influence; it is possible to start by eliminating {circumflex over (D)} by making Û_(i)·Û₁ ^(T)=Ĝ·{circumflex over (K)}_(i)·{circumflex over (K)}₁ ^(T)·Ĝ^(T) and to likewise solve.

This first configuration 102, which is able to correct up to six degrees of freedom, requires, by way of operating constraints, the minimum number N of measurements to be higher than or equal to 3, and the axes of the rotations Û_(i) to be distinct for at least three different values of the index “i”.

In FIG. 4 and in a second configuration 202, which is degraded with respect to the nominal configuration 102, a first step 204 of acquiring measurements is implemented. This first step 204 implements same first step 104 of acquiring N measurements of rotation matrices {circumflex over (K)}_(l), which matrices are calculated with measurement stations that are identical to those of the nominal configuration, but it is here assuming that, for the calculated matrices {circumflex over (K)}_(l), the azimuth value is inexact or not calculated, or in any case inexploitable.

This poor knowledge of the azimuth value is expressed mathematically by writing, in the first step, that, for any i, varying from 1 to N, the matrix {circumflex over (K)}_(i) may be decomposed as follows: {circumflex over (K)}_(i)={circumflex over (Ψ)}_(i)·{circumflex over (Q)}_(i), where

{circumflex over (Ψ)}_(i) is an unknown rotation matrix of elementary azimuthal form:

$\begin{pmatrix} {\cos \; \psi \; i} & {{- \sin}\; \psi \; i} & 0 \\ {\sin \; \psi \; i} & {\cos \; \psi \; i} & 0 \\ 0 & 0 & 1 \end{pmatrix};$

and

{circumflex over (Q)}_(i) is a known rotation matrix.

Thus, the general starting equations become:

Û _(i) =Ĝ·{circumflex over (Ψ)} _(i) ·{circumflex over (Q)} _(i) ·{circumflex over (D)} for i varying from 1 to N.

In a second step 206, the system of equations that was described above is reduced and solved, to determine the right bias matrix {circumflex over (D)}, by implementing a second subset 212 of the following substeps.

In a fourth substep 214, a pivot measurement is created, for example a pivot first measurement corresponding to i equal to 1.

For i=2, . . . , N, it may be verified that: Û₁ ^(T)·Û_(i)={circumflex over (D)}^(T)·{circumflex over (Q)}₁ ^(T)·{circumflex over (Ψ)}₁ ^(T)·{circumflex over (Ψ)}_(i)·{circumflex over (Q)}_(i)·{circumflex over (D)}.

By noting for i=2, . . . , N, Ψ_(1,i)={circumflex over (Ψ)}₁ ^(T)·{circumflex over (Ψ)}_(i), which are unknown rotation matrices of elementary azimuthal form, and Û_(1,i)=Û₁ ^(T)·Û_(i), the following system of equations is obtained:

{circumflex over (Q)} ₁ ·{circumflex over (D)}·Û _(1,i) ·{circumflex over (D)} ^(T) ·{circumflex over (Q)} _(i) ^(T)={circumflex over (Ψ)}_(1,i), i varying from 2 to N.

In a second substep, to eliminate the unknown matrices {circumflex over (Ψ)}_(1,i), the fact that said matrices {circumflex over (Ψ)}_(1,i) are of elementary azimuthal form and that they leave the vector

$\overset{\rightarrow}{k} = \begin{pmatrix} 0 \\ 0 \\ 1 \end{pmatrix}$

unchanged, i.e. they respect the following equations:

${{\begin{pmatrix} {\cos \; \psi} & {{- \sin}\; \psi} & 0 \\ {\sin \; \psi} & {\cos \; \psi} & 0 \\ 0 & 0 & 1 \end{pmatrix}\begin{pmatrix} 0 \\ 0 \\ 1 \end{pmatrix}} = \begin{pmatrix} 0 \\ 0 \\ 1 \end{pmatrix}},$

i varying from 2 to N, is used.

Therefore, for each and every i=2, . . . ,N: {circumflex over (Q)}₁·{circumflex over (D)}·Û_(1,i)·{circumflex over (D)}^(T)·{circumflex over (Q)}_(i) ^(T)·{right arrow over (k)}={right arrow over (k)}, which will be written:

Û_(1,i)·{circumflex over (D)}^(T)·{circumflex over (Q)}_(i) ^(T)·{right arrow over (k)}={circumflex over (D)}^(T)·{circumflex over (Q)}₁ ^(T)·{right arrow over (k)}.

Noting {right arrow over (d)}={circumflex over (D)}^(T)·Q₁ ^(T)·k, which is therefore an unknown vector, and q_(i)=Q_(i) ^(T)·k, which for their part are known vectors, the following system of equations to be solved is obtained:

Û _(1,i) ·{circumflex over (D)} ^(T) ·{right arrow over (q)} _(i) ={right arrow over (d)} for each and every i=2, . . . ,N.

In the same fourth substep 214, for i=2, . . . ,N, the matrices Û_(1,i) and the vectors {right arrow over (q)}_(i) are calculated using the following equations:

Û _(1,i) =Û ₁ ^(T) ·Û _(i) and {right arrow over (q)}_(i)={circumflex over (Q)}_(i) ^(T)·{right arrow over (k)}

Next, in the fifth, sixth and seventh substeps 216, 218, 220, the system of equations: {right arrow over (q)}_(i)={right arrow over (d)} for each and every i=2, . . . , N, is solved iteratively using the first tool O1 and the third tool O3.

In a fifth substep 216, a first sequence of matrices {{circumflex over (D)}_([s])}, [s] designating the current index of a term {circumflex over (D)}_([s]) of the sequence, is initialized by setting {circumflex over (D)}_([0]) equal to I₃, I₃being the identity matrix.

Next, in the iterative sixth substep 218 in which iteration [s+1] is passed to from iteration [s] by calculating the vector value {right arrow over (d)}_([s+1]), then the value {circumflex over (D)}_([s+1]) of the first matrix sequence {{circumflex over (D)}_([s])}, using the following recurrence relationships:

${\overset{\rightarrow}{d}}_{\lbrack{s + 1}\rbrack} = \frac{\sum_{i \geq 2}\left( {{\hat{U}}_{1,i} \cdot {\hat{D}}_{\lbrack s\rbrack}^{T} \cdot {\overset{\rightarrow}{q}}_{i}} \right)}{{\sum_{i \geq 2}\left( {{\hat{U}}_{1,i} \cdot {\hat{D}}^{T} \cdot {\overset{\rightarrow}{q}}_{i}} \right)}}$ ${\hat{D}}_{\lbrack{s + 1}\rbrack} = {\pi\left( {\sum\limits_{i \geq 2}\left( {{\overset{\rightarrow}{q}}_{i} \cdot {\overset{\rightarrow}{d}}_{\lbrack{s + 1}\rbrack}^{T} \cdot {\hat{U}}_{1,i}} \right)} \right)}$

{circumflex over (D)} is calculated as being a limit or an approximate limit of the sequence {circumflex over (D)}_([s]), which is convergent.

In a seventh substep 220, the iterative process carried out throughout the sixth substep 218 is stopped when the limit {circumflex over (D)} is approximated with a sufficient precision defined by a preset threshold value.

Next, in the second step 206, the system of equations: {circumflex over (Q)}₁·{circumflex over (D)}·Û_(1,i)·{circumflex over (D)}^(T)·{circumflex over (Q)}_(i) ^(T)={circumflex over (Ψ)}_(1,i), i varying from 1 to N, is reduced and solved, to determine the left bias matrix Ĝ, by implementing a set of substeps analogous to the second set 212, by creating a pivot on the right.

This second configuration 202 requires, by way of operating constraints, the minimum number N of measurements to be higher than or equal to 4, and the axes of the rotations Û_(i) to be distinct for at least three different values of the index “i”.

In FIG. 5 and in a third configuration 302, which is degraded with respect to the nominal first configuration 102, a first step 304 of acquiring measurements is carried out in which N measurements of raw rotation matrices {circumflex over (K)}_(l) are performed by the DDP posture-detecting subsystem 16.

These measurements of raw rotation matrices {circumflex over (K)}_(l), varying from 1 to N, correspond to targeting actions Vi in which a plurality of different targeting directions {right arrow over (x_(l))} of the viewing device D_(v) serving as sight are respectively aligned with a plurality of different directions {right arrow over (y_(l))} that are known in the reference exterior coordinate system R_(Ref) without roll adjustment, i.e. without rotation of the head about the line of sight.

For example, the pilot targets with various cross-shaped reticles, displayed on the sight D_(v), various preset directions that are known in the reference exterior coordinate system R_(Ref) without roll adjustment.

In this measuring first step 304, the N rotator matrices {circumflex over (K)}_(i) measured and calculated by the posture-detecting subsystem 16 are entirely known, i.e. all their components are known. The two families of normalized or direction vectors {{right arrow over (x)}_(i)} and {{right arrow over (y)}_(i)} are also assumed to be free and to allow the general system of dual harmonization equations to be reduced to the particular system of dual harmonization equations:

{right arrow over (y)} _(i) =Ĝ·{circumflex over (K)} _(i) ·{circumflex over (D)}·{right arrow over (x)} _(i), varying from 1 to N.

Next, in a second step 306, the system of dual harmonization equations: y_(i)=G·K_(i)·{circumflex over (D)}·x_(i) for i varying from 1 to N, is reduced and solved iteratively by using two times the second tool O2 and by implementing a third set 312 of the following substeps.

In an eighth substep 314, a first sequence of left matrices {Ĝ_([s])}, [s] designating the integer rank of advancement through this first sequence, is initialized by setting Ĝ_([0]) equal I₃, I₃ being the identity matrix.

Next, an iterative ninth substep 316 is repeated, in which substep iteration [s+1] is passed to from iteration [s] by calculating the matrix value {circumflex over (D)}_([s+1]) then the matrix value Ĝ_([s+1]) using the following equations:

${\hat{D}}_{\lbrack{s + 1}\rbrack} = {\pi\left( {\sum\limits_{i \geq 1}\left( {{\hat{K}}_{i}^{T} \cdot {\hat{G}}_{\lbrack s\rbrack}^{T} \cdot {\overset{\rightarrow}{y}}_{i} \cdot {\overset{\rightarrow}{x}}_{i}^{T}} \right)} \right)}$ ${\hat{G}}_{\lbrack{s + 1}\rbrack} = {\pi\left( {\sum\limits_{i \geq 1}\left( {{\overset{\rightarrow}{y}}_{i} \cdot {\overset{\rightarrow}{x}}_{i}^{T} \cdot {\hat{D}}_{\lbrack{s + 1}\rbrack}^{T} \cdot {\hat{K}}_{i}^{T}} \right)} \right)}$

the sequence {{circumflex over (D)}_([s])} being a second sequence of right matrices.

The sequences {circumflex over (D)}_([s]) and Ĝ_([s]) converge to {circumflex over (D)} and Ĝ, respectively.

In a tenth substep 318, the iterative process executed throughout the ninth substep 316 is stopped when the limits {circumflex over (D)} and Ĝ are approximated with a sufficient precision.

This third configuration requires, by way of operating constraints, the minimum number N of measurements to be higher than or equal to 4, and the vector families {{right arrow over (x)}_(i)} and {{right arrow over (y)}_(i)} both to be free.

In FIG. 6 and in a fourth configuration 402, which is degraded with respect to the nominal first configuration 102, a first step 404 of acquiring N measurements of raw rotation matrices {circumflex over (K)}_(l) is executed.

The N raw rotation matrices {circumflex over (K)}_(l), which are measured by the posture-detecting subsystem, correspond to a plurality of targeting actions Vi that are more constrained than the targeting actions performed in the third configuration 302.

The targeting actions Vi of the fourth configuration 402 correspond to an alignment of N different targeting directions {right arrow over (x)}_(l) of the sight D_(v) with one and the same direction {right arrow over (y₀)}, which direction is known in the exterior reference coordinate system R_(ref), without roll adjustment, i.e. without rotation of the head about the line of sight. For example, the pilot targets with various cross-shaped reticles of the sight, one and the same preset direction, which direction is known in the reference exterior coordinate system, without roll adjustment.

In this fourth configuration 402, it is then only possible to calculate the right bias rotation matrix {circumflex over (D)} and the left bias rotation matrix Ĝ is assumed to be known.

In this measuring first step 404, the N rotation matrices {circumflex over (K)}_(l), which are measured and calculated by the posture-detecting subsystem 16, are entirely known, i.e. all their components are known. Assuming the family of normalized or direction vectors {{right arrow over (x)}_(i)} of the sight to also be free, and the targeted external unit vector {right arrow over (y₀)} to be known and the left bias rotation matrix Ĝ to be known, the general system of dual harmonization equations reduces to the particular system of dual harmonization equations:

Ĝ·{circumflex over (K)} _(i) ·{circumflex over (D)}·{right arrow over (x)} _(i) ={right arrow over (y)} ₀, i varying from 1 to N.

Therefore, only the right bias rotation matrix {circumflex over (D)} is sought.

Next, in a second step 406, the system of dual harmonization equations: Ĝ·{circumflex over (K)}_(i)·{circumflex over (D)}·{right arrow over (x)}_(i)={right arrow over (y)}₀, for i varying from 1 to N, is reduced and solved, and the sought right matrix {circumflex over (D)}is determined via the following equation:

$\hat{D} = {\pi\left( {\sum\limits_{i \geq 1}\left( {{\hat{K}}_{i}^{T} \cdot {\hat{G}}^{T} \cdot {\overset{\rightarrow}{y}}_{0} \cdot {\overset{\rightarrow}{x}}_{i}^{T}} \right)} \right)}$

This fourth configuration requires, by way of operating constraints, the minimum number N of measurements to be higher than or equal to 3 and the vector family {{right arrow over (x)}_(i)} to be free.

It will be noted that, with the targeting method of the fourth configuration 402, it is not possible, knowing {circumflex over (D)}, to calculate Ĝ. Specifically, knowing Ĝ, it is easy to show that a suitable choice of the freedoms in the family {{right arrow over (x)}_(i)} will allow the operator Σ_(i≥1)({circumflex over (K)}_(i) ^(T)·G^(T)·{right arrow over (y)}₀·{right arrow over (x)}_(i) ^(T)) to be made reversible, i.e. of rank 3, and therefore, via rectification thereof, {circumflex over (D)} to be found. In contrast, if {circumflex over (D)} is assumed to be known, G must necessarily be the rectified form of the operator Σ_(i≥1)({right arrow over (y)}₀·{right arrow over (x)}_(i) ^(t)·{circumflex over (D)}^(T)·{circumflex over (K)}_(i) ^(T)); however, this operator is at best of rank 1, and therefore its rank is insufficient because its image is either zero, or reduced to the straight line expressed by {right arrow over (y)}₀.

In FIG. 7 and in a fifth configuration 502, which is degraded with respect to the nominal first configuration 102, a first step of acquiring N measurements is carried out in which N rotation matrices {circumflex over (K)}_(l) are calculated by the posture-detecting device.

The N calculated rotation matrices {circumflex over (K)}_(l) correspond to N measurement stations or targeting actions Vi that differ from those of the fourth configuration 402 in that the coordinates of the targeted exterior direction {right arrow over (y)}₀ are unknown.

The targeting actions Vi of the fifth configuration 502 correspond to an alignment of N different targeting directions {right arrow over (x_(l))} of the sight D_(v) with one and the same exterior direction {right arrow over (y₀)} the coordinates of which are unknown, without roll adjustment, i.e. without rotation of the head about the targeting line. For example, the pilot targets with various cross-shaped reticles of the sight one and the same unknown external direction without roll adjustment.

In this fifth configuration, it is still possible to only calculate the right rotation matrix {circumflex over (D)}, but it is also possible to calculate the coordinates of the exterior targeting direction if it is desired to do so.

In this measuring first step 504, the N rotation matrices {circumflex over (K)}_(l) which are measured and calculated by the posture-detecting subsystem 16, are entirely known, i.e. all their components are known. Assuming the family of normalized or direction vectors {{right arrow over (x)}_(i)} to also be free, and the targeted external unit vector {right arrow over (y₀)} to be unknown and the left bias rotation matrix Ĝ to be known, the general system of dual harmonization equations reduces to the particular system of dual harmonization equations:

Ĝ·{circumflex over (K)} _(i) ·{circumflex over (D)}·{right arrow over (x)} _(i) ={right arrow over (y)} ₀, varying from 1 to N.

Only the right rotation matrix {circumflex over (D)}, and if it is desired the targeted exterior direction, which direction is expressed in the reference external coordinate system R_(Ref), may be determined.

In a second step 506, the system of dual harmonization equations: {right arrow over (G)}·{circumflex over (K)}_(i){circumflex over (D)}·{right arrow over (x)}_(i)={right arrow over (y)}₀ for i varying from 1 to N, is solved iteratively by implementing a fifth set 512 of the following eleventh, twelfth and thirteenth substeps 514, 516, 518.

In the eleventh substep 514, a first sequence of right matrices {{circumflex over (D)}_([s])}, [s] designating the integer rank of advancement through the sequence {{circumflex over (D)}_([s])}, is initialized by setting {circumflex over (D)}_([0]) equal to I₃, I₃ being the identity matrix.

Next, the iterative twelfth substep 516 is repeated, in which substep iteration [s+1] is passed to from iteration [s] by calculating the vector ŷ_([s+1]) then the matrix {circumflex over (D)}_([s+1]) using the following equations:

${\overset{\rightarrow}{y}}_{\lbrack{s + 1}\rbrack} = \frac{\sum_{i \geq 1}\left( {\hat{G} \cdot {\hat{K}}_{i} \cdot {\hat{D}}_{\lbrack s\rbrack} \cdot {\hat{x}}_{i}} \right)}{{\sum_{i \geq 1}\left( {\hat{G} \cdot {\hat{K}}_{i} \cdot {\hat{D}}_{\lbrack s\rbrack} \cdot {\hat{x}}_{i}} \right)}}$ ${\hat{D}}_{\lbrack{s + 1}\rbrack} = {\pi\left( {\sum\limits_{i \geq 1}\left( {{\hat{K}}_{i}^{T} \cdot {\hat{G}}^{T} \cdot {\overset{\rightarrow}{y}}_{\lbrack{s + 1}\rbrack} \cdot {\overset{\rightarrow}{x}}_{i}^{T}} \right)} \right)}$

the sequence {{right arrow over (y)}_([s])} being a second sequence of external direction vectors.

The sequences {{right arrow over (y)}_([s])} and {{circumflex over (D)}_([s])} converge to {right arrow over (y₀)} and {circumflex over (D)}, respectively.

In the thirteenth step 518, the iterative process carried out throughout the twelfth substep 516 is stopped when the limits {circumflex over (D)} and Ĝ are approximated with a sufficient precision, defined by one or two preset threshold values.

This fifth configuration requires, by way of operating constraints, the minimum number N of measurements to be higher than or equal to 4, and the vector family {{right arrow over (x)}_(i)} to be free.

In FIG. 8 and in a sixth configuration 602, which is degraded with respect to the nominal first configuration 102, a first step 604 of acquiring N measurements is carried out in which N rotation matrices {circumflex over (K)}_(l) are calculated by the posture-detecting device 16.

The N calculated rotation matrices {circumflex over (K)}_(l) here correspond to N targeting actions Vi that are identical to those of the fifth configuration 502 in that N alignments of targeting direction {right arrow over (x)}_(i) are carried out with one and the same targeted exterior direction {right arrow over (y₀)} without roll adjustment, and in that the targeted exterior direction {right arrow over (y₀)} is unknown, but that differ from those of the fifth configuration 502 in that the left bias rotation matrix is unknown.

In this sixth configuration 602, it is still possible to only calculate the right rotation matrix {circumflex over (D)}, but it is also possible to calculate the coordinates of the unknown targeted exterior direction {right arrow over (y₀)}.

The N measured and calculated rotation matrices {circumflex over (K)}_(l) are assumed to be entirely known, i.e. all their components are known. The family of known normalized or direction vectors {{right arrow over (x)}_(i)} of the sight and the unknown unit vector {right arrow over (y₀)} of the targeted external direction are related in the system of dual harmonization equations: Ĝ·{circumflex over (K)}_(i)·{circumflex over (D)}·{right arrow over (x)}_(i)={right arrow over (y)}₀, for each and every i=1 to N, the matrix Ĝ being unknown, and only the right bias rotation matrix {circumflex over (D)} being able to be determined.

By noting {right arrow over (z)}₀=Ĝ^(t)·{right arrow over (y)}₀, for i equal to 1 to N, the equations G·K_(i){circumflex over (D)}·x_(i)=y₀ are reduced to the system of dual harmonization equations:

{circumflex over (K)} _(i) ·{circumflex over (D)}·{right arrow over (x)} _(i) ={right arrow over (z)} ₀, for i equal to 1 to N.

In a second step 604, the system of equations {circumflex over (K)}_(i)·{circumflex over (D)}·{right arrow over (x)}_(i)={right arrow over (z)}₀ for i varying from 1 to N with {right arrow over (z)}₀=Ĝ^(T)·{right arrow over (y)}₀, is solved iteratively by implementing a sixth set 612 of the following substeps.

In a fourteenth substep 614, a first sequence of right matrices {{circumflex over (D)}_([s])}, [s] designating the integer rank of advancement through the sequence {{circumflex over (D)}_([s])}, is initialized by setting {circumflex over (D)}_([0]) equal to I₃, I₃ being the identity matrix.

Next, an iterative fifteenth substep 616 is repeated, in which substep iteration [s+1] is passed to from iteration [s] by calculating the vector {right arrow over (z)}_([s+1]) then the matrix {circumflex over (D)}_([s+1]) using the following equations:

${\overset{\rightarrow}{z}}_{\lbrack{s + 1}\rbrack} = \frac{\sum_{i \geq 1}\left( {{\hat{K}}_{i} \cdot {\hat{D}}_{\lbrack s\rbrack} \cdot {\overset{\rightarrow}{x}}_{i}} \right)}{{\sum_{i \geq 1}\left( {{\hat{K}}_{i} \cdot {\hat{D}}_{\lbrack s\rbrack} \cdot {\overset{\rightarrow}{x}}_{i}} \right)}}$

${\hat{D}}_{\lbrack{s + 1}\rbrack} = {\pi\left( {\sum\limits_{i \geq 1}\left( {{\hat{K}}_{i}^{T} \cdot {\overset{\rightarrow}{z}}_{\lbrack{s + 1}\rbrack} \cdot {\overset{\rightarrow}{x}}_{i}^{T}} \right)} \right)}$

the sequence {{right arrow over (z)}_([s])} being an auxiliary second sequence of external direction vectors and the sequences {{circumflex over (D)}_([s]) } converging to {circumflex over (D)}.

Next, in a sixteenth step 616, the iterative process carried out throughout the fifteenth substep 614 is stopped when the limit {circumflex over (D)} is approximated with a sufficient precision defined by a threshold value.

This sixth configuration 602 requires, by way of operating constraints, the minimum number N of measurements to be higher than or equal to 4, and the vector family {{right arrow over (x)}_(i)} to be free.

Just as in the fifth configuration 502, with this targeting method 602 it is not possible to calculate Ĝ knowing {circumflex over (D)}.

In FIG. 9 and in a seventh configuration 702, which is degraded with respect to the nominal first configuration, a first step 704 of acquiring N measurements is carried out, in which step N raw DDP rotation matrices {circumflex over (K)}_(l) are calculated by the posture-detecting subsystem 16.

The N measured and calculated rotation matrices {circumflex over (K)}_(l) correspond to N targeting actions Vi, i varying from 1 to N, in which one and the same targeting direction {right arrow over (x₀)} on the sight is aligned with a plurality of targeted or aimed at or pointed exterior directions, without taking into account roll of the head.

For example, the pilot targets with a single cruciform reticle of position that is known in the coordinate system R_(v) of the sight, a plurality of preset exterior directions {right arrow over (y_(l))} in the reference exterior coordinate system R_(Ref), without roll adjustment, i.e. without performing a rotation about the line of sight. It is then possible to only calculate the right rotation matrix {circumflex over (D)}, the left rotation matrix Ĝ being assumed to be known.

The N measured rotation matrices {circumflex over (K)}_(i), which are assumed to be entirely known, i.e. all their components are assumed to be known, the family of the normalized vectors {{right arrow over (y)}_(i)} of the targeted exterior directions, which is assumed to be known, and the known unit vector {right arrow over (x₀)} of the single targeting direction are related by the system of dual harmonization equations: Ĝ·{circumflex over (K)}_(i)·{circumflex over (D)}·{right arrow over (x)}₀={right arrow over (y)}_(i) for each and every i=1 to N, in which system of equations the right rotation matrix {circumflex over (D)} is known and the left matrix Ĝ is sought.

Next, in a second step 706, the system of dual harmonization equations: Ĝ·{circumflex over (K)}_(i)·{circumflex over (D)}·{right arrow over (x)}₀={right arrow over (y)}_(i), for i varying from 1 to N, is solved by determining the sought left rotation matrix Ĝ using the equation:

$\hat{G} = {\pi\left( {\sum\limits_{i \geq 1}\left( {{\overset{\rightarrow}{y}}_{i} \cdot {\overset{\rightarrow}{x}}_{0}^{T} \cdot {\hat{D}}^{T} \cdot {\hat{K}}_{i}^{T}} \right)} \right)}$

This seventh configuration 702 requires, by way of operating constraints, the minimum number N of measurements to be higher than or equal to 3 and the vector family {{right arrow over (y)}_(i)} to be free.

In the FIG. 10 and in an eighth configuration 802, which is degraded with respect to the nominal first configuration 102, a first step 804 of acquiring N measurements is carried out, in which step N rotation matrices {circumflex over (K)}_(l) are calculated by the posture-detecting device.

The N measured and calculated rotation matrices {circumflex over (K)}_(l) correspond to N targeting actions Vi that are identical to those of the seventh configuration 702 in that N alignments are carried out of one and the same targeting direction {right arrow over (x₀)} on the sight and of a plurality of targeted or aimed at or pointed to exterior directions that are known, without taking into account roll of the head, and in that the right rotation matrix {circumflex over (D)} is known, but that differ from those of the seventh configuration 702 in that the targeting direction {right arrow over (x₀)} is unknown.

The N measured rotation matrices {circumflex over (K)}_(i), which are assumed to be entirely known, i.e. all their components are known, the family of normalized vectors {{right arrow over (y)}_(i)} of the targeted exterior directions, which is assumed to be known, and the unknown unit vector {right arrow over (x₀)} of the single targeted direction are related by the system of dual harmonization equations: Ĝ·{circumflex over (K)}_(i)·{circumflex over (D)}·{right arrow over (x)}₀={right arrow over (y)}_(i), for each and every i=1 to N, in which system of equations the right rotation matrix {circumflex over (D)} is known and the left matrix G and optionally the sight targeting direction are sought.

In this eighth configuration 802, it is possible to only calculate the left rotation matrix Ĝ, though the coordinates of the single targeting direction {right arrow over (x₀)} in the sight coordinate system may also be calculated.

Next, in a second step 806, the system of dual harmonization equations: Ĝ·{circumflex over (K)}_(i)·{circumflex over (D)}·{right arrow over (x)}₀={right arrow over (y)}_(i) for i varying from 1 to N, is solved iteratively by implementing an eighth set of the following substeps.

In a seventeenth substep 814, a first sequence of left matrices {Ĝ_([s])}, [s] designating the integer rank of advancement through the sequence {Ĝ_([s])}, is initialized by setting Ĝ_([0]) equal to I₃, I₃ being the identity matrix.

Next, an iterative eighteenth substep 816 is repeated, in which substep iteration [s+1] is passed to from iteration [s] by calculating the vector {right arrow over (x)}_([s+1]), then the matrix Ĝ_([s+1]) using the following equations:

${\overset{\rightarrow}{x}}_{\lbrack{s + 1}\rbrack} = \frac{\sum_{i \geq 1}\left( {{\hat{D}}^{T} \cdot {\hat{K}}_{i}^{T} \cdot {\hat{G}}_{\lbrack s\rbrack}^{T} \cdot {\overset{\rightarrow}{y}}_{i}} \right)}{{\sum_{i \geq 1}\left( {{\hat{D}}^{T} \cdot {\hat{K}}_{i}^{T} \cdot {\hat{G}}_{\lbrack s\rbrack}^{T} \cdot {\overset{\rightarrow}{y}}_{i}} \right)}}$ ${\hat{G}}_{\lbrack{s + 1}\rbrack} = {\pi\left( {\sum\limits_{i \geq 1}\left( {{\overset{\rightarrow}{y}}_{i} \cdot {\overset{\rightarrow}{x}}_{\lbrack{s + 1}\rbrack}^{T} \cdot {\hat{D}}^{T} \cdot {\hat{K}}_{i}^{T}} \right)} \right)}$

the sequence {{right arrow over (x)}_([s])} being a second sequence of sight direction vectors.

The sequences Ĝ_([s]) and {right arrow over (x)}×_([s]) then converge to Ĝ and {right arrow over (x)}₀, respectively.

In a nineteenth substep 818, the iterative process carried out throughout the eighteenth substep 816 is stopped when the limit Ĝ and optionally the limit {right arrow over (x)}₀ are approximated with a sufficient precision defined by one or two preset threshold values.

This eighth configuration 802 requires, by way of operating constraints, the minimum number N of measurements to be higher than or equal to 4 and the vector family {{right arrow over (y)}_(i)} to be free.

It will be noted that the solving method described for the above seven degraded configurations is generalizable to any other configuration of the same type.

It will be noted that the invention also allows a harmonized relative deviation between the outputs delivered by two DDP posture-detecting systems that are tightly fastened to each other to be delivered.

The first DDP detecting system delivering the rotation {circumflex over (R)}(R_(v1)/R_(ref1)) between a first sight coordinate system R_(v1) and a first fixed exterior coordinate system R_(ref1), and the harmonized second posture-detecting system {circumflex over (R)}(R_(v2)/R_(ref2)) delivering the rotation between a second sight coordinate system R_(v2) and a second fixed exterior coordinate system R_(ref2), the method according to the invention allows the rotation matrix {circumflex over (R)}(R_(v2)/R_(v1)) of the rotation between the first sight coordinate system R_(v1) and the second sight coordinate system R_(v2) to be calculated as a left matrix, and the rotation matrix {circumflex over (R)}(R_(ref2)/R_(ref1)) of the rotation between the first fixed exterior coordinate system R_(ref1) and the second fixed coordinate system R_(ref2) to be calculated as a right matrix.

Specifically, the problem is mathematically equivalent to the preceding one since it is possible to write:

{circumflex over (R)}(R _(v2)/R _(ref2))={circumflex over (R)}(R _(ref2) /R _(ref1))^(T) ·{circumflex over (R)}(R _(v1) /R _(ref1))·{circumflex over (R)}(R _(v2) /R _(v1)),

Ĝ={circumflex over (R)}(R _(ref2) /R _(ref1))^(T) and {circumflex over (D)}={circumflex over (R)}(R _(v2) /R _(v1)) are then sought.

Likewise, in the case where it is sought to determine the relative deviation between two tightly fastened DDP systems, the measurements delivered by each of the DDPs do not need to be complete.

Regarding the algorithmic method for achieving global DDP harmonization and the variants thereof described above, the essential features are:

-   -   the universal and generic character of the Tr rectifying method         used, which allows each and every solvable case to be treated         with matrix mathematics, without ever having to make use of         elaborate mathematical functions, in particular trigonometric         functions;     -   the flexibility of application of the rectification Tr, which in         essence allows problems to be reduced independently from the         order of the elements to be treated.

Regarding the global harmonization of a posture detection implemented by a posture-detecting system or the characterization of a deviation between the posture detections delivered by two posture-detecting systems using the algorithmic harmonization process according to the invention, the essential features are:

-   -   the fact that it is possible to completely harmonize the DDP         posture-detecting method and system without needing to perform         partial harmonizations of each element, which each time require         exact knowledge of the posture of the other element, and which         in practice transfer residual errors;     -   the fact that it is possible to completely harmonize the DDP         posture-detecting method and system without knowing beforehand         which element or elements are poorly aligned;     -   the fact that it is possible to harmonize the posture-detecting         method and system without the expected data or measurements         being integrally known.

Generally, the head-up viewing system 2 described above and configured to implement the dual harmonization method according to the invention is intended to be located on-board a carrier vehicle comprised in the set of all aircraft, aeroplanes, helicopters, motor vehicles and robots. 

1. A method for dual harmonization of a DDP posture-detecting subsystem integrated into a worn/borne head-up viewing system, the worn/borne head-up viewing system being located on-board a carrier vehicle and comprising: a transparent worn/borne head-up viewing device D_(v), an exterior reference device D_(ref) having an exterior reference coordinate system R_(ref), possibly either a coordinate system of the carrier vehicle or a local geographic coordinate system or a terrestrial coordinate system; a DDP posture-detecting subsystem comprising: a tracking solid first element S1 tightly attached to the viewing device D_(v); a fixed solid second element S2 tightly joined to the reference device D_(f), and a means for measuring and determining the relative orientation {circumflex over (K)} of the tracking mobile first element S1 with respect to the fixed second element S2, a dual harmonization subsystem for harmonizing the worn/borne head-up viewing system and the DDP posture-detecting subsystem, the dual harmonization method being wherein it comprises steps consisting in in a first step, a series of a preset number N of measurements of relative orientations {circumflex over (K)}_(l), i varying from 1 to N, of the tracking mobile first element S1 with respect to the fixed second element S2 of the DDP posture-detecting subsystem, corresponding to different targeting actions Vi, i varying from 1 to N, are carried out, in which measurements one or more different preset elements of pilot/driver information displayed in the viewing device D_(v) are superposed or aligned with one or more corresponding landmarks of the real outside world the theoretical rotation matrices Û_(i) of which in the exterior reference coordinate system are known; then in a second step, and using a dual harmonization algorithm, conjointly calculating the relative orientation matrix {circumflex over (R)}(S1/v) of the tracking first element S1 of the posture-detecting subsystem with respect to the viewing device D_(v) and/or the relative orientation matrix {circumflex over (R)}(ref/S2) of the external reference device D_(Ref) with respect to the fixed solid second element S2 of the posture-detecting subsystem to respectively be the right-side bias rotation matrix {circumflex over (D)} and the left-side bias rotation matrix Ĝ, which are conjoint solutions of the system of dual harmonization equations: Û _(i) =Ĝ·{circumflex over (K)} _(i) ·{circumflex over (D)}, i varying from 1 to N.
 2. The method for dual harmonization of a DDP posture-detecting subsystem integrated into a worn/borne head-up viewing system according to claim 1, wherein the minimum required number N of measurements depends on the number of erroneous or inexploitable degrees of angular freedom of the rotation matrices {circumflex over (R)}(S1/v) and {circumflex over (R)}(ref/S2) of the head-up viewing system, said number L being an integer higher than or equal to 1 and lower than or equal to 6, and the solution of the system of equations Û_(i)=Ĝ·{circumflex over (K)}_(i)·{circumflex over (D)}, i varying from 1 to N, uses a rectification operator π(.) that converts any given matrix A into a 3×3 square rotation matrix π(A), which matrix π(A), of all the 3×3 rotation matrices, is the closest in the least-squares sense to all of the terms of the matrix π(A)−A, to determine the right-side rotation {circumflex over (D)} and the left-side rotation Ĝ.
 3. The method for dual harmonization of a DDP posture-detecting subsystem integrated into a worn/borne head-up viewing system according to claim 2, wherein and in a first configuration, the number of erroneous or inexploitable degrees of angular freedom of the right-side bias rotation matrix {circumflex over (D)} is equal to three and the number of erroneous or inexploitable degrees of angular freedom of the left-side bias rotation matrix G is equal to three, the first step carries out a number N higher than or equal to 3 of measurements, for which measurements the targeting actions Vi correspond to an alignment of displayed three-dimensional reference marks with observed exterior three-dimensional reference marks, and the second step of solving the system of dual harmonization equations comprises a first set of substeps consisting in: in a first substep, choosing a “pivot” measurement as the first measurement among the N measurements, this pivot measurement corresponding to i equal to 1, and for i=2, . . . , N the rotation matrices Û_(1,i) and {circumflex over (K)}_(1,i) are calculated using the equations: Û_(1,i)=Û₁ ^(T)·Û_(i) and {circumflex over (K)}_(1,i)={circumflex over (K)}₁ ^(T)·K_(i); then in a second substep, determining for i=2, . . . , N the principle unit vectors of the rotations Û_(1,i) and {circumflex over (K)}_(1,i), designated by {right arrow over (u)}_(i) and {right arrow over (k)}_(i), respectively; then in a third substep, calculating the right matrix {circumflex over (D)} using the equation: $\hat{D} = {\pi\left( {\sum\limits_{i \geq 2}\left( {{\overset{\rightarrow}{k}}_{i} \cdot {\overset{\rightarrow}{u}}_{i}^{T}} \right)} \right)}$ then in a fourth substep, determining the left-side rotation matrix Ĝ on the basis of the matrix {circumflex over (D)} calculated in the third substep, using the equation: $\hat{G} = {\pi\left( {\sum\limits_{i \geq 1}\left( {{\hat{U}}_{i} \cdot {\hat{D}}^{T} \cdot {\hat{K}}_{i}^{T}} \right)} \right)}$
 4. The method for dual harmonization of a DDP posture-detecting subsystem integrated into a worn/borne head-up viewing system according to claim 2, wherein and in a second configuration, the number of erroneous or inexploitable degrees of angular freedom of the right-side bias rotation matrix {circumflex over (D)} is equal to three and the single erroneous or inexploitable degree of angular freedom of the left-side bias rotation matrix Ĝ is the azimuth angle, the elevation and roll angles being assumed to be known with a sufficient precision; and the first step carries out a number N higher than or equal to 4 of measurements, for which measurements the targeting actions Vi correspond to an alignment of displayed three-dimensional reference marks with observed three-dimensional reference marks, and the second step of solving the system of dual harmonization equations comprises a second set of substeps consisting in: in a fourth substep for i=2, . . . ,N, calculating the matrices Û_(1,i) and the vectors {right arrow over (q)}_(i) using the equations: Û _(1,i) =Û ₁ ^(T) ·U _(i) and {right arrow over (q)} _(i) ={circumflex over (Q)} _(i) ^(T) ·{right arrow over (k)}, the vector {right arrow over (k)} being defined by the equation ${\overset{\rightarrow}{k} = \begin{pmatrix} 0 \\ 0 \\ 1 \end{pmatrix}};$ then in an initialization fifth substep, initializing a first sequence of matrices {{circumflex over (D)}_([s])}, [s] designating the current integer rank of advancement through the sequence {{circumflex over (D)}_([s])}, by setting {circumflex over (D)}_([0]) equal to I₃, I₃ being the identity matrix; then repeating an iterative sixth substep in which iteration [s+1] is passed to from iteration [s] by calculating the vector value {right arrow over (d)}_([s+1]), then the value {circumflex over (D)}_([s+1]) of the first matrix sequence {{circumflex over (D)}_([s])}, using the following equations: ${\overset{\rightarrow}{d}}_{\lbrack{s + 1}\rbrack} = \frac{\sum_{i \geq 2}\left( {{\hat{U}}_{1,i} \cdot {\hat{D}}_{\lbrack s\rbrack}^{T} \cdot {\overset{\rightarrow}{q}}_{i}} \right)}{{\sum_{i \geq 2}\left( {{\hat{U}}_{1,i} \cdot {\hat{D}}^{T} \cdot {\overset{\rightarrow}{q}}_{i}} \right)}}$ ${\hat{D}}_{\lbrack{s + 1}\rbrack} = {\pi\left( {\sum\limits_{i \geq 2}\left( {{\overset{\rightarrow}{q}}_{i} \cdot {\overset{\rightarrow}{d}}_{\lbrack{s + 1}\rbrack}^{T} \cdot {\hat{U}}_{1,i}} \right)} \right)}$ the sequence {{right arrow over (d)}_([s])} being an auxiliary second sequence of vectors and the sequence {{circumflex over (D)}_([s])} converging to {circumflex over (D)}; and stopping in a seventh substep the iterative process carried out throughout the sixth substep when the limit {circumflex over (D)} is approximated with a sufficient precision defined by a preset threshold value.
 5. The method for dual harmonization of a DDP posture-detecting subsystem integrated into a worn/borne head-up viewing system according to claim 2, wherein and in a third configuration, the number of erroneous or inexploitable degrees of angular freedom of the right-side bias rotation matrix{circumflex over (D)} is equal to three and the number of erroneous or inexploitable degrees of angular freedom of the left-side bias rotation matrix G is equal to three, and the first step carries out a number N higher than or equal to 4 of measurements, for which measurements the targeting actions Vi correspond to an alignment of a plurality of different targeting directions {right arrow over (x)}_(l) with a plurality of targeted exterior directions {right arrow over (y_(l))} that are known in the reference exterior coordinate system R_(Ref), without roll adjustment, the vector families {{right arrow over (x)}_(i)} and {{right arrow over (y)}_(i)} both being free; and the second step of solving the system of dual harmonization equations: {right arrow over (y)}_(i)=Ĝ·{circumflex over (K)}_(i)·{circumflex over (D)}·{right arrow over (x)}_(i) for i varying from 1 to N comprises a third set of the following substeps consisting in: in an initialization eighth substep, initializing a first sequence of left matrices {Ĝ_([s])}, [s] designating the integer rank of advancement through this first sequence, by setting Ĝ_([0]) equal to I₃, I₃ being the identity matrix; then repeating an iterative ninth substep in which iteration [s+1] is passed to from iteration [s] by calculating the matrix {circumflex over (D)}_([s+1]) then the matrix Ĝ_([s+1]) using the following equations: ${\hat{D}}_{\lbrack{s + 1}\rbrack} = {\pi\left( {\sum\limits_{i \geq 1}\left( {{\hat{K}}_{i}^{T} \cdot {\hat{G}}_{\lbrack s\rbrack}^{T} \cdot {\overset{\rightarrow}{y}}_{i} \cdot {\overset{\rightarrow}{x}}_{i}^{T}} \right)} \right)}$ ${\hat{G}}_{\lbrack{s + 1}\rbrack} = {\pi\left( {\sum\limits_{i \geq 1}\left( {{\overset{\rightarrow}{y}}_{i} \cdot {\overset{\rightarrow}{x}}_{i}^{T} \cdot {\hat{D}}_{\lbrack{s + 1}\rbrack}^{T} \cdot {\hat{K}}_{i}^{T}} \right)} \right)}$ the sequence {{circumflex over (D)}_([s])} being a second sequence of right matrices, and the sequences {circumflex over (D)}_([s])and Ĝ_([s]) converging to {circumflex over (D)} and Ĝ, respectively; and stopping in a stopping tenth substep the iterative process executed throughout the ninth substep when the limits {circumflex over (D)} and Ĝ are approximated with a sufficient precision.
 6. The method for dual harmonization of a DDP posture-detecting subsystem integrated into a worn/borne head-up viewing system according to claim 2, wherein and in a fourth configuration, the number of erroneous or inexploitable degrees of angular freedom of the right-side bias rotation matrix {circumflex over (D)} is equal to three and the left-side bias rotation matrix Ĝ is assumed to be known, and the first step carries out a number N higher than or equal to 3 of measurements, for which measurements the targeting actions Vi correspond to an alignment of N different targeting directions {right arrow over (x)}_(i) with one and the same targeted direction {right arrow over (y₀)}, which targeted direction is known in the reference exterior coordinate system R_(Ref), without roll adjustment, the vector family {{right arrow over (x)}_(i)} being free; and the second step of solving the system of dual harmonization equations: Ĝ·Ĝ_(i)·{circumflex over (D)}·{right arrow over (x)}_(i)={right arrow over (y)}₀ for i varying from 1 to N determines the right bias rotation matrix {circumflex over (D)} via the following equation: $\hat{D} = {\pi\left( {\sum\limits_{i \geq 1}\left( {{\hat{K}}_{i}^{T} \cdot {\hat{G}}^{T} \cdot {\overset{\rightarrow}{y}}_{0} \cdot {\overset{\rightarrow}{x}}_{i}^{T}} \right)} \right)}$
 7. The method for dual harmonization of a DDP posture-detecting subsystem integrated into a worn/borne head-up viewing system according to claim 2, wherein and in a fifth configuration, the number of erroneous or inexploitable degrees of angular freedom of the right-side bias rotation matrix {circumflex over (D)} is equal to three and the left-side bias rotation matrix Ĝ is assumed to be known, and the first step carries out a number N higher than or equal to 4 of measurements, for which measurements the targeting actions Vi correspond to an alignment of N different targeting directions {right arrow over (x)}_(i) with one and the same unknown targeted exterior direction {right arrow over (y₀)}, without roll adjustment, the vector family {{right arrow over (x)}_(i)} being free; and the second step of solving the system of dual harmonization equations: Ĝ·{circumflex over (K)}_(i)·{circumflex over (D)}·{right arrow over (x)}_(i)={right arrow over (y)}₀ for i varying from 1 to N comprises a fifth set of substeps consisting in: in an initialization eleventh substep, initializing a first sequence of right matrices {{circumflex over (D)}_([s])}, [s] designating the integer rank of advancement through the sequence {{circumflex over (D)}_([s])}, by setting {circumflex over (D)}_([0]) equal to I₃, I₃ being the identity matrix; then repeating an iterative twelfth substep in which iteration [s+1] is passed to from iteration [s] by calculating the vector {right arrow over (y)}_([s+1]) then the matrix {circumflex over (D)}_([s+1]) using the following equations: ${\overset{\rightarrow}{y}}_{\lbrack{s + 1}\rbrack} = \frac{\sum_{i \geq 1}\left( {\hat{G} \cdot {\hat{K}}_{i} \cdot {\hat{D}}_{\lbrack s\rbrack} \cdot {\overset{\rightarrow}{x}}_{i}} \right)}{{\sum_{i \geq 1}\left( {\hat{G} \cdot {\hat{K}}_{i} \cdot {\hat{D}}_{\lbrack s\rbrack} \cdot {\overset{\rightarrow}{x}}_{i}} \right)}}$ ${\hat{D}}_{\lbrack{s + 1}\rbrack} = {\pi\left( {\sum\limits_{i \geq 1}\left( {{\hat{K}}_{i}^{T} \cdot {\hat{G}}^{T} \cdot {\overset{\rightarrow}{y}}_{\lbrack{s + 1}\rbrack} \cdot {\overset{\rightarrow}{x}}_{i}^{T}} \right)} \right)}$ the sequence {{right arrow over (y)}_([s])} being a second sequence of external direction vectors, and the sequences {{right arrow over (y)}_([s])} and {{circumflex over (D)}_([s])} converging to {right arrow over (y₀)} and {circumflex over (D)}, respectively; and stopping in a stopping thirteenth substep the iterative process carried out throughout the twelfth substep when the limits {right arrow over (y₀)} and {circumflex over (D)} are approximated with a sufficient precision defined by one or two preset threshold values.
 8. The method for dual harmonization of a DDP posture-detecting subsystem integrated into a worn/borne head-up viewing system according to claim 2, wherein and in a sixth configuration, the number of erroneous or inexploitable degrees of angular freedom of the right-side bias rotation matrix {circumflex over (D)} is equal to three and the left-side bias rotation matrix Ĝ is unknown and indeterminable, and the first step carries out a number N higher than or equal to 4 of measurements, for which measurements the targeting actions Vi correspond to an alignment of N different targeting directions {right arrow over (x)}_(i) with one and the same unknown targeted exterior direction {right arrow over (y₀)}, without roll adjustment, the vector family {{right arrow over (x)}_(i)} being free, and reduces the solution of the system of dual harmonization equations: Ĝ·{circumflex over (K)}_(i)·{circumflex over (D)}·{right arrow over (x)}_(i)={right arrow over (y)}₀ for i varying from 1 to N to the solution of the reduced system of dual harmonization equations: {circumflex over (K)} _(i) ·{circumflex over (D)}·{right arrow over (x)} _(i) ={right arrow over (z)} ₀ for i varying from 1 to 4, noting {right arrow over (z)}₀=Ĝ^(T)·{right arrow over (y)}₀; and the second step of solving the reduced system of dual harmonization equations comprises a sixth set of substeps consisting in: in an initialization fourteenth substep, initializing a first sequence of right matrices {{circumflex over (D)}_([s])}, [s] designating the integer rank of advancement through the sequence {{circumflex over (D)}_([s])}, {circumflex over (D)}_([0]) being set equal to I₃, I₃ being the identity matrix; then repeating an iterative fifteenth substep in which iteration [s+1] is passed to from iteration [s] by calculating the vector {right arrow over (z)}_([s+1]) then the matrix {circumflex over (D)}_([s+1]) of the first matrix sequence using the following equations: ${\overset{\rightarrow}{z}}_{\lbrack{s + 1}\rbrack} = \frac{\sum_{i \geq 1}\left( {{\hat{K}}_{i} \cdot {\hat{D}}_{\lbrack s\rbrack} \cdot {\overset{\rightarrow}{x}}_{i}} \right)}{{\sum_{i \geq 1}\left( {{\hat{K}}_{i} \cdot {\hat{D}}_{\lbrack s\rbrack} \cdot {\overset{\rightarrow}{x}}_{i}} \right)}}$ ${\hat{D}}_{\lbrack{s + 1}\rbrack} = {\pi\left( {\sum\limits_{i \geq 1}\left( {{\hat{K}}_{i}^{T} \cdot {\overset{\rightarrow}{z}}_{\lbrack{s + 1}\rbrack} \cdot {\overset{\rightarrow}{x}}_{i}^{T}} \right)} \right)}$ the sequence {{right arrow over (z)}_([s])} being a second auxiliary sequence of vectors and the sequence {{circumflex over (D)}_([s])} converging to {circumflex over (D)}, and stopping in a stopping sixteenth substep the iterative process carried out throughout the fifteenth substep when the limit {circumflex over (D)} is approximated with a sufficient precision defined by a preset threshold value.
 9. The method for dual harmonization of a DDP posture-detecting subsystem integrated into a worn/borne head-up viewing system according to claim 2, wherein and in a seventh configuration, the number of erroneous or inexploitable degrees of angular freedom of the left-side bias rotation matrix Ĝ is equal to three and the right-side bias rotation matrix {circumflex over (D)} is assumed to be known; and the first step carries out a number N higher than or equal to 3 of measurements, for which measurements the targeting actions Vi correspond to an alignment of one and the same known targeting direction {right arrow over (x)}₀ with N known targeted exterior directions {right arrow over (y_(l))}, without roll adjustment, the vector family {{right arrow over (y)}_(i)} being free, and the second step of solving the system of dual harmonization equations: Ĝ·{circumflex over (K)}_(i)·{circumflex over (D)}·{right arrow over (x)}₀={right arrow over (y)}_(i) for i varying from 1 to N determines the sought left rotation matrix Ĝ using the equation: $\hat{G} = {\pi\left( {\sum\limits_{i \geq 1}\left( {{\overset{\rightarrow}{y}}_{i} \cdot {\overset{\rightarrow}{x}}_{0}^{T} \cdot {\hat{D}}^{T} \cdot {\hat{K}}_{i}^{T}} \right)} \right)}$
 10. The method for dual harmonization of a DDP posture-detecting subsystem integrated into a worn/borne head-up viewing system according to claim 2, wherein and in an eighth configuration, the number of erroneous or inexploitable degrees of angular freedom of the left-side bias rotation matrix Ĝ is equal to three and the right-side bias rotation matrix {circumflex over (D)} is assumed to be known, and the first step carries out a number N higher than or equal to 4 of measurements, for which measurements the targeting actions Vi correspond to an alignment of one and the same unknown targeting direction {right arrow over (x)}₀ with N known targeted exterior directions {right arrow over (y_(l))}, without roll adjustment, the vector family {{right arrow over (y)}_(i)} being free; and the second step of solving the system of dual harmonization equations: Ĝ·{circumflex over (K)}_(i)·{circumflex over (D)}·{right arrow over (x)}₀={right arrow over (y)}_(i) for i varying from 1 to N comprises an eighth set of substeps consisting in: in a seventeenth substep, initializing a first sequence of left matrices {Ĝ_([s])}, [5] designating the integer rank of advancement through the sequence {Ĝ_([s])}, Ĝ_([0]) being initialized set equal to I₃, I₃ being the identity matrix; then repeating an iterative eighteenth substep in which iteration [s+1] is passed to from iteration [s] by calculating the vector {right arrow over (x)}_([s+1]) then the matrix Ĝ_([s+1]) using the following equations: ${\overset{\rightarrow}{x}}_{\lbrack{s + 1}\rbrack} = \frac{\sum_{i \geq 1}\left( {{\hat{D}}^{T} \cdot {\hat{K}}_{i}^{T} \cdot {\hat{G}}_{\lbrack s\rbrack}^{T} \cdot {\overset{\rightarrow}{y}}_{i}} \right)}{{\sum_{i \geq 1}\left( {{\hat{D}}^{T} \cdot {\hat{K}}_{i}^{T} \cdot {\hat{G}}_{\lbrack s\rbrack}^{T} \cdot {\overset{\rightarrow}{y}}_{i}} \right)}}$ ${\hat{G}}_{\lbrack{s + 1}\rbrack} = {\pi\left( {\sum\limits_{i \geq 1}\left( {{\overset{\rightarrow}{y}}_{i} \cdot {\overset{\rightarrow}{x}}_{\lbrack{s + 1}\rbrack}^{T} \cdot {\hat{D}}^{T} \cdot {\hat{K}}_{i}^{T}} \right)} \right)}$ the sequence {{right arrow over (x)}_([s])} being a second sequence of sight direction vectors, the sequences Ĝ_([s]) and {right arrow over (x)}_([s]) converging to Ĝ and {right arrow over (x)}₀, respectively; and in a stopping nineteenth substep stopping the iterative process carried out throughout the eighteenth substep when the limits Ĝ and optionally {right arrow over (x)}₀ are approximated with a sufficient precision defined by one or two preset threshold values.
 11. The method for dual harmonization of a DDP posture-detecting subsystem integrated into a worn/borne head-up viewing system according to claim 1, wherein the worn/borne head-up viewing system is intended to be located on-board a carrier vehicle comprised in the set of all aircraft, aeroplanes, helicopters, motor vehicles and robots.
 12. A worn/borne head-up viewing system located on-board a carrier vehicle and comprising: a transparent worn/borne head-up viewing device D_(v), a reference device D_(ref) having a reference coordinate system R_(ref), possibly either a coordinate system of the carrier vehicle or a local geographic coordinate system or a terrestrial coordinate system; a DDP posture-detecting subsystem comprising: a tracking solid first element S1 tightly attached to the viewing device D_(v), a fixed solid second element S2 tightly joined to the reference device D_(ref), and a means for measuring and determining the relative orientation {circumflex over (K)} of the tracking mobile first element S1 with respect to the fixed second element S2, a dual harmonization subsystem for harmonizing the head-up viewing system and the DDP posture-detecting subsystem, the dual harmonization subsystem comprising a dual harmonization processor and an HMI interface for managing the acquisitions of the harmonization measurements, the worn/borne head-up viewing system being wherein the dual harmonization subsystem and the DDP posture-detecting subsystem are configured to: in a first step, carry out a series of a preset number N of measurements of relative orientations {circumflex over (K)}_(l), i varying from 1 to N, of the tracking mobile first element S1 with respect to the fixed second element S2 of the DDP posture-detecting subsystem, corresponding to different targeting actions Vi, i varying from 1 to N, in which measurements one or more different preset elements of pilot/driver information displayed in the viewing device D_(v) are superposed or aligned with one or more corresponding landmarks of the real outside world; then in a second step, and using a dual harmonization algorithm, conjointly calculate the relative orientation matrix {circumflex over (R)}(S1/v) of the tracking first element S1 of the posture-detecting subsystem with respect to the viewing device D_(v) and/or the relative orientation {circumflex over (R)}(ref /S2) of the external reference device D_(Ref) with respect to the fixed solid second element S2 of the posture-detecting subsystem to respectively be the right-side bias rotation matrix D and the left-side bias rotation matrix Ĝ, which are conjoint solutions of the system of dual harmonization equations: Û _(i) =Ĝ·{circumflex over (K)} _(i) ·{circumflex over (D)}, i varying from 1 to N.
 13. The worn/borne head-up viewing system located on-board a carrier vehicle according to claim 12, wherein the minimum required number N of measurements depends on the number L of erroneous or inexploitable degrees of angular freedom of the rotation matrices {circumflex over (R)}(S1/v) and {circumflex over (R)}(ref/S2) of the head-up viewing system, said number L being an integer higher than or equal to 1 and lower than or equal to 6, and the solution of the system of equations Û_(i)=Ĝ·{circumflex over (K)}_(i)·{circumflex over (D)}, i varying from 1 to N, uses a rectification operator π(.) that converts any given matrix A into a 3×3 square rotation matrix π(A), which matrix π(A), of all the 3×3 rotation matrices, is the closest in the least-squares sense to all of the terms of the matrix π(A)−A, to determine the right-side rotation {circumflex over (D)} and the left-side rotation Ĝ.
 14. A worn/borne head-up viewing system located on-board a carrier vehicle and comprising: a transparent worn/borne head-up viewing device D_(v), a reference device D_(ref) having a reference coordinate system R_(ref), possibly either a coordinate system of the carrier vehicle or a local geographic coordinate system or a terrestrial coordinate system; a DDP posture-detecting subsystem comprising: a tracking solid first element S1 tightly attached to the viewing device D_(v), a fixed solid second element S2 tightly joined to the reference device D_(ref), and a means for measuring and determining the relative orientation {circumflex over (K)} of the tracking mobile first element S1 with respect to the fixed second element S2, a dual harmonization subsystem for harmonizing the head-up viewing system and the DDP posture-detecting subsystem, the dual harmonization subsystem comprising a dual harmonization processor and an HMI interface for managing the acquisitions of the harmonization measurements, the worn/borne head-up viewing system being wherein the dual harmonization subsystem and the DDP posture-detecting subsystem are configured to: in a first step, carry out a series of a preset number N of measurements of relative orientations {circumflex over (K)}_(l), varying from 1 to N, of the tracking mobile first element S1 with respect to the fixed second element S2 of the DDP posture-detecting subsystem, corresponding to different targeting actions Vi, i varying from 1 to N, in which measurements one or more different preset elements of pilot/driver information displayed in the viewing device D_(v) are superposed or aligned with one or more corresponding landmarks of the real outside world; then in a second step, and using a dual harmonization algorithm, conjointly calculate the relative orientation matrix {circumflex over (R)}(S1/v) of the tracking first element S1 of the posture-detecting subsystem with respect to the viewing device D_(v) and/or the relative orientation matrix {circumflex over (R)}(ref/S2) of the external reference device D_(Ref) with respect to the fixed solid second element S2 of the posture-detecting subsystem to respectively be the right-side bias rotation matrix D and the left-side bias rotation matrix Ĝ, which are conjoint solutions of the system of dual harmonization equations: Û _(i) =Ĝ·{circumflex over (K)} _(i) ·{circumflex over (D)}, i varying from 1 to N; the minimum required number N of measurements depends on the number L of erroneous or inexploitable degrees of angular freedom of the rotation matrices {circumflex over (R)}(S1/v) and {circumflex over (R)}(ref/S2) of the head-up viewing system, said number L being an integer higher than or equal to 1 and lower than or equal to 6, the solution of the system of equations Û_(i)=Ĝ·{circumflex over (K)}_(i)·{circumflex over (D)}, i varying from 1 to N, uses a rectification operator π(.) that converts any given matrix A into a 3×3 square rotation matrix π(A), which matrix π(A), of all the 3×3 rotation matrices, is the closest in the least-squares sense to all of the terms of the matrix π(A)−A, to determine the right-side rotation {circumflex over (D)} and the left-side rotation Ĝ; and wherein the dual harmonization subsystem and the DDP posture-detecting subsystem are configured to implement the first and second steps such as defined in claim
 3. 15. A carrier vehicle, comprised in the set of all aircraft, aeroplanes, helicopters, motor vehicles and robots, and in which is installed a worn/borne head-up viewing system defined according to claim
 12. 